mit mechanical engineering phd program

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Department of Mechanical Engineering

Mechanical engineering is concerned with the responsible development of products, processes, and power, at scales ranging from molecules to large and complex systems. Mechanical engineering principles and skills are involved at some stage during the conception, design, development, and manufacture of every human-made object with moving parts. Many innovations crucial to our future will have their roots in the world of mass, motion, forces, and energy—the world of mechanical engineers.

Mechanical engineering is one of the broadest and most versatile of the engineering professions. This is reflected in the portfolio of current activities in the Department of Mechanical Engineering (MechE), one that has widened rapidly in the past decade. Today, our faculty are involved in a wide range of projects, including designing tough hydrogels, using nanostructured surfaces for clean water and thermal management of microelectronics, developing efficient methods for robust design, the building of robotics for land and underwater exploration, creating optimization methods that autonomously generate decision-making strategies, developing driverless cars, inventing cost-effective photovoltaic cells, developing thermal and electrical energy storage systems, using acoustics to explore the ocean of one of Jupiter's moons, studying the biomimetics of swimming fish for underwater sensing applications, developing physiological models for metastatic cancers, inventing novel medical devices, exploring 3D printing of nanostructures and macrostructures, and developing coatings to create nonstick surfaces.

The department carries out its mission with a focus on the seven areas of excellence described below. Our education and research agendas are informed by these areas, and these are the areas in which we seek to impassion the best undergraduate and graduate students.

Area 1: Mechanics: Modeling, Experimentation, and Computation (MMEC). At the heart of mechanical engineering lies the ability to measure, describe, and model the physical world of materials and mechanisms. The MMEC area focuses on teaching the fundamental principles, essential skills, and scientific tools necessary for predicting thermo-mechanical phenomena and using such knowledge in rational engineering design. We provide students with the foundations in experimental, modeling, and computational skills needed to understand, exploit, and enhance the thermo-physical behavior of advanced engineering devices and systems, and to make lifelong creative contributions at the forefront of the mechanical sciences and beyond. Research in the MMEC area focuses on four key thrusts:

• Computational mechanics
• Fluid dynamics and transport
• Mechanics of solid materials
• Nonlinear dynamics

The fundamental engineering principles embodied in these topics can be applied over a vast range of force, time, and length scales, and applications of interest in the MMEC area span the spectrum from the nano/micro world to the geophysical domain. A Course 2-A track is offered in this area.

Area 2: Design, Manufacturing, and Product Development. Design, manufacturing, and product development is the complete set of activities needed to bring new devices and technologies to the marketplace. These activities span the entire product life-cycle, from the identification of a market opportunity or need, through design, testing, manufacture and distribution, and end of useful life. Our work includes everything from understanding the voice of the customer to finding new ways of processing materials to improving product performance and tracking product flow through a distribution network. A central component of this area is the design and construction of novel equipment, either for consumer products or for industrial uses. This spans scales from meters to microns, and involves mechanical, electronic and electromechanical devices. Many MechE students apply design, manufacturing, and product development skills and techniques to extracurricular design work for organizations and student activities such as Design that Matters, Formula SAE, Satellite Engineering Team, and the Solar Electric Vehicle Team. Some projects lead to flagship products for new companies. A Course 2-A track in product development is offered along with a unique Master of Engineering degree in manufacturing.

Area 3: Controls, Instrumentation, and Robotics. The mission in this area is to promote research and education for automating, monitoring, and manipulating systems. The focus is on system-level behavior that emerges primarily from interactions and cannot be explained from individual component behavior alone. We seek to identify fundamental principles and methodologies that enable systems to exhibit intelligent, goal-oriented behavior, and develop innovative instruments to monitor, manipulate, and control systems. The core competencies in which we seek to excel are:

• Methodologies for understanding system behavior through physical modeling, identification, and estimation.
• Technologies for sensors and sensor networks; actuators and energy transducers; and systems for monitoring, processing, and communicating information.
• Fundamental theories and methodologies for analyzing, synthesizing, and controlling systems; learning and adapting to unknown environments; and effectively achieving task goals.

We seek to apply our core competencies to diverse areas of social, national, and global needs. These include health care, security, education, medical and security related imaging, space and ocean exploration, and autonomous systems in air, land, and underwater environments. We also offer a Course 2-A track in this area.

Area 4: Energy Science and Engineering. Energy is one of the most significant challenges facing humanity and is a central focus of mechanical engineering's contribution to society. Our research focuses on efficient and environmentally friendly energy conversion and utilization from fossil and renewable resources. Programs in the department cover many of the fundamental and technological aspects of energy, with applications to high performance combustion engines, batteries and fuel cells, thermoelectricity and photovoltaics, wind turbines, and efficient buildings. Work in very-low-temperature thermodynamics includes novel sub-Kelvin refrigeration. Efforts in high-temperature thermodynamics and its coupling with transport and chemistry include internal combustion engine analysis, design, and technology; control of combustion dynamics and emissions; thermoelectric energy conversion; low- and high-temperature fuel cells; and novel materials for rechargeable batteries and thermal energy storage. Work in heat and mass transport covers thermal control of electronics from manufacturing to end use; microscale and nanoscale transport phenomena; desalination and water purification; high heat flux engineering; and energy-efficient building technology. Work in renewable energy encompasses the design of offshore and floating wind turbines and tidal wave machines; and analysis and manufacturing of photovoltaic and thermophotovoltaic devices. Energy storage, hybrid systems, fuel synthesis, and integration of energy systems are active research areas in the department. We also offer a Course 2-A track in energy.

Area 5: Ocean Science and Engineering. The oceans cover over 70 percent of the planet's surface and constitute a critical element in our quality of life, including the climate and the resources and food that we obtain from the sea. This area's objectives are to support the undergraduate and graduate programs in ocean engineering, including the naval construction program, the MIT/Woods Hole Oceanographic Institution Joint Program in Applied Oceanography and the Course 2-OE degree in mechanical and ocean engineering. It also serves as the focus point of ocean-related research and education at MIT. Major current research activities include marine robotics and navigation of underwater vehicles and smart sensors for ocean mapping and exploration; biomimetics to extract new understanding for the development of novel ocean systems studying marine animals; the study of the mechanics and fluid mechanics of systems for ultradeep ocean gas and oil extraction; ocean wave and offshore wind energy extraction; the free surface hydrodynamics of ocean-going vehicles; the development of advanced naval and commercial ships and submersibles, including the all-electric ship; the mechanics and crashworthiness of ocean ships and structures; ocean transportation systems; ocean acoustics for communication, detection, and mapping in the ocean; and adaptive sampling and multidisciplinary forecasting of the ocean behavior. The design of complex ocean systems permeates all these areas and provides the cohesive link for our research and teaching activities.

Area 6: Bioengineering. Engineering analysis, design, and synthesis are needed to understand biological processes and to harness them successfully for human use. Mechanical forces and structures play an essential role in governing the function of cells, tissues, and organs. Our research emphasizes integration of molecular-to-systems–level approaches to probe the behavior of natural biological systems, and to design and build new systems, ranging from analysis of gene regulatory networks to microfluidic assays for drug screening or new technologies for quantitative, high-throughput biomedical imaging. Emphasis is also placed on creating new physiological or disease models, including multicellular engineered living systems, using nano- and micro-fabrication as well as new biomaterials. Applications include understanding, diagnosing, and treating diseases such as atherosclerosis, osteoarthritis, spinal cord injury or liver failure; new tools for drug discovery and drug development; and tissue-engineered scaffolds and devices for in vivo regeneration of tissues and organs. Work also includes design and fabrication of new devices and tools for rehabilitation of stroke victims and for robotic surgery. We offer many elective subjects at the undergraduate and graduate levels, as well as a bioengineering track in Course 2-A.

Area 7: Nano/Micro Science and Technology. The miniaturization of devices and systems of ever-increasing complexity has been a fascinating and productive engineering endeavor during the past few decades. Near and long term, this trend will be amplified as physical understanding of the nano world expands, and widespread commercial demand drives the application of manufacturing to micro- and nanosystems. Micro- and nanotechnology can have tremendous impact on a wide range of mechanical systems. Examples include microelectromechanical system (MEMS) devices and products that are already deployed as automobile airbag sensors, smart phone parts, and for drug delivery; stronger and lighter nanostructured materials now used in airplanes and automobiles; and nanostructured energy conversion devices that significantly improve the efficiency of renewable energy systems. Research in this area cuts across mechanical engineering and other disciplines. Examples include sensors and actuators; micro-fluidics, heat transfer, and energy conversion at the micro- and nanoscales; optical and biological micro- and nano-electromechanical systems (MEMS and NEMS); engineered nanomaterials; atomic scale precision engineering; and the nano-phoptonics in measurement, sensing, and systems design. Students interested in micro/nano technology are encouraged to explore the Course 2-A nanoengineering track.

In order to prepare the mechanical engineers of the future, the department has developed undergraduate and graduate educational programs of the depth and breadth necessary to address the diverse and rapidly changing technological challenges that society faces. Our educational programs combine the rigor of academic study with the excitement and creativity inherent to innovation and research.

Bachelor of Science in Mechanical Engineering (Course 2)

Bachelor of science in engineering (course 2-a), bachelor of science in mechanical and ocean engineering (course 2-oe), minor in mechanical engineering, undergraduate study.

The Department of Mechanical Engineering (MechE) offers three programs of undergraduate study. The first of these, the traditional program that leads to the bachelor's degree in mechanical engineering, is a more structured program that prepares students for a broad range of career choices in the field of mechanical engineering. The second program leads to a bachelor's degree in engineering and is intended for students whose career objectives require greater flexibility. It allows them to combine the essential elements of the traditional mechanical engineering program with study in another, complementary field. The third program, in mechanical and ocean engineering, is also a structured program for students interested in mechanical engineering as it applies to the engineering aspects of ocean science, exploration, and utilization, and of marine transportation.

All of the educational programs in the department prepare students for professional practice in an era of rapidly advancing technology. They combine a strong base in the engineering sciences (mechanics, materials, fluid and thermal sciences, systems and control) with project-based laboratory and design experiences. All strive to develop independence, creative talent, and leadership, as well as the capability for continuing professional growth.

The program in mechanical engineering provides a broad intellectual foundation in the field of mechanical engineering. The program develops the relevant engineering fundamentals, includes various experiences in their application, and introduces the important methods and techniques of engineering practice.

The educational objectives of the program leading to the degree Bachelor of Science in Mechanical Engineering are that:

Within a few years of graduation, a majority of our graduates will have completed or be progressing through top graduate programs; advancing in leadership tracks in industry, non-profit organizations, or the public sector; or pursuing entrepreneurial ventures. In these roles they will: (1) apply a deep working knowledge or technical fundamentals in areas related to mechanical, electromechanical, and thermal systems to address needs of the customer and society; (2) develop innovative technologies and find solutions to engineering problems; (3) communicate effectively as members of multidisciplinary teams; (4) be sensitive to professional and societal contexts and committed to ethical action; (5) lead in the conception, design, and implementation of new products, processes, services, and systems.

Students are urged to contact the MechE Undergraduate Office as soon as they have decided to enter mechanical engineering so that a faculty advisor may be assigned. Students, together with their faculty advisors, plan a program that best utilizes the departmental electives and the 48 units of unrestricted electives available in the Course 2 degree program.

This program is accredited by the Engineering Accreditation Commission of the Accreditation Board for Engineering and Technology (ABET)  as a mechanical engineering degree.

Course 2-A is designed for students whose academic and career goals demand greater breadth and flexibility than are allowed under the mechanical engineering program, Course 2. To a large extent, the 2-A program allows students an opportunity to tailor a curriculum to their own needs, starting from a solid mechanical engineering base. The program combines a rigorous grounding in core mechanical engineering topics with an individualized course of study focused on a second area that the student designs with the help and approval of the 2-A faculty advisor. The program leads to the degree Bachelor of Science in Engineering.

This program is accredited by the Engineering Accreditation Commission of ABET as an engineering degree.

The educational objectives of the program leading to the degree of Bachelor of Science in Engineering are that:

A significant part of the 2-A curriculum consists of electives chosen by the student to provide in-depth study of a field of the student's choosing. A wide variety of popular concentrations are possible in which well-selected academic subjects complement a foundation in mechanical engineering and general Institute requirements. Some examples of potential concentrations include robotics, engineering management, product development, biomedical engineering and pre-medicine, energy conversion engineering, sustainable development, architecture and building technology, and any of the seven departmental focus areas mentioned above. The MechE faculty have developed specific recommendations in some of these areas; details are available from the MechE Undergraduate Office and on the departmental website.

Concentrations are not limited to those listed above. Students are encouraged to design and propose technically oriented concentrations that reflect their own needs and those of society.

The student's overall program must contain a total of at least one and one-half years of engineering content (150 units) appropriate to the student's field of study. The required core and second-level subjects include approximately 78 units of engineering topics. The self-designed concentration must include at least 72 more units of engineering topics. While engineering topics are usually covered through engineering subjects, subjects outside the School of Engineering may provide material essential to the engineering program of some concentrations. For example, management subjects usually form an essential part of an engineering management concentration. In all cases, the relationship of concentration subjects to the particular theme of the concentration must be obvious.

To pursue the 2-A degree, students must submit the online 2-A enrollment form no later than Add Date of their second term in the program.

This program is intended for students who are interested in combining a firm foundation in mechanical engineering with a specialization in ocean engineering. The program includes engineering aspects of the ocean sciences, ocean exploration, and utilization of the oceans for transportation, defense, and extracting resources. Theory, experiment, and computation of ocean systems and flows are covered in a number of subjects, complementing a rigorous mechanical engineering program; a hands-on capstone design class allows students to master the design of advanced marine systems, including autonomous underwater vehicles and smart sensors.

This program is accredited by the Engineering Accreditation Commission of ABET in both mechanical engineering and ocean engineering.

The educational objectives of the program leading to the degree Bachelor of Science in Mechanical and Ocean Engineering are that within a few years of graduation, a majority of our graduates will have completed or be progressing through top graduate programs; advancing in leadership tracks in industry, non-profit organizations, or the public sector; or pursuing entrepreneurial ventures. In these roles they will: (1) apply a deep working knowledge or technical fundamentals in areas related to mechanical, electromechanical, and thermal systems to address needs of the customer and society; (2) develop innovative technologies and find solutions to engineering problems; (3) communicate effectively as members of multidisciplinary teams; (4) be sensitive to professional and societal contexts and committed to ethical action; (5) lead in the conception, design, and implementation of new products, processes, services, and systems.

Graduates have exciting opportunities in offshore industries, naval architecture, the oceanographic industry, the Navy or government, or for further study in graduate school.

Students pursuing a minor in the department must complete a total of six 12-unit subjects in the Mechanical Engineering Department program. At least three of the subjects must be selected from among the required subjects for the Course 2 and Course 2-OE degree programs, which are listed below. In addition, two subjects may be selected from restricted electives in those programs. 

Further information on undergraduate programs may be obtained from the MechE Undergraduate Office , Room 1-110, 617-253-230.

Master of Science in Mechanical Engineering

Master of science in ocean engineering/master of science in naval architecture and marine engineering/master of science in oceanographic engineering, master of engineering in advanced manufacturing and design, mechanical engineer's degree, naval engineer's degree—program in naval construction and engineering, doctor of philosophy and doctor of science, graduate study.

The Department of Mechanical Engineering (MechE) provides opportunities for graduate work leading to the following degrees: Master of Science in Mechanical Engineering, Master of Science in Ocean Engineering, Master of Science in Naval Architecture and Marine Engineering, Master of Science in Oceanographic Engineering, Master of Engineering in Manufacturing, degree of Mechanical Engineer, degree of Naval Engineer, and the Doctor of Philosophy (PhD) or Doctor of Science (ScD), which differ in name only.

The Master of Engineering in Manufacturing degree is a 12-month professional degree intended to prepare students for technical leadership in the manufacturing industries.

The Mechanical Engineer's and Naval Engineer's degrees offer preparation for a career in advanced engineering practice through a program of advanced coursework that goes well beyond the master's level. These degrees are not a stepping stone to the PhD.

The Doctor of Philosophy (or Science), the highest academic degree offered, is awarded upon the completion of a program of advanced study and significant original research, design, or development.

Admission Requirements for Graduate Study

Applications to the mechanical engineering graduate program are accepted from persons who have completed, or will have completed by the time they arrive, a bachelor's degree if they are applying for a master's degree, or a master's degree if they are applying for a PhD. Most incoming students have a degree in mechanical engineering or ocean engineering, or some related branch of engineering. The department's admission criteria are not specific, however, and capable students with backgrounds in different branches of engineering or in science may gain entry. Nevertheless, to qualify for a graduate degree, the candidate is expected to have had at least an undergraduate-level exposure to the core subject areas in mechanical engineering (applied mechanics, dynamics, fluid mechanics, thermodynamics, materials, control systems, and design) and to be familiar with basic electrical circuits and electromagnetic field theory.

Applications for September entry are due on December 15 of the previous year and decisions are reported in March. International students applying from abroad may be admitted, but they will be allowed to register only if they have full financial support for the first year.

All applicants to the graduate program in mechanical engineering must submit the GRE test results. International students whose native language is not English are required to take either the International English Language Testing System (IELTS) exam and receive a minimum score of 7 or the TOEFL exam with a minimum acceptable score of 577 (PBT), 233 (CBT) or 100 (iBT).

Early Admission to Master's Degree Programs in Mechanical Engineering

At the end of the junior year, extraordinarily qualified students in the Department of Mechanical Engineering will be invited to apply for early admission to the graduate program. Students who are admitted will then be able to enroll in core graduate subjects during the senior year and to find a faculty advisor who is willing to start and supervise research for the master's thesis while the student is still in the senior year. With the consent of the faculty advisor, the student may also use a portion of the work conducted towards the master's thesis in the senior undergraduate year to satisfy the requirements of the bachelor's thesis.

Writing Ability Requirement

The Mechanical Engineering Department requires that all incoming graduate students demonstrate satisfactory English writing ability, or successfully complete appropriate training in writing. This requirement reflects the faculty's conviction that writing is an essential skill for all engineers. All incoming graduate students, native as well as international, must take the departmental writing ability test, which is administered online in June. Depending on the results, a student will either pass or be required to take a short course during the Independent Activities Period (IAP) in January.

To qualify for the Master of Science in Mechanical Engineering, a student must complete at least 72 credits of coursework, not including thesis. Of these, at least 48 must be graduate subjects (refer to the Guide to Graduate Study [PDF] on the MechE website). The remainder of the 72 units may include advanced undergraduate subjects that are not requirements in the undergraduate mechanical engineering curriculum.

At least three of the graduate subjects must be taken in mechanical engineering sciences (refer to the Guide to Graduate Study [PDF] on the MechE website). Students must take at least one graduate mathematics subject (12 units) offered by the MIT Mathematics Department. For the Master of Science in Oceanographic Engineering, see also the requirements listed in the Joint Program with Woods Hole Oceanographic Institution.

Finally, a thesis is required. The thesis is an original work of research, development, or design, performed under the supervision of a faculty or research staff member, and is a major part of any graduate program in the Mechanical Engineering Department. A master's student usually spends as much time on thesis work as on coursework. A master's degree usually takes about one and one-half to two years to complete.

The requirements for each of these three degrees are that the student takes 72 credit units of graduate subjects and complete a thesis.

At least three of the subjects must be chosen from a prescribed list of ocean engineering subjects (refer to the Guide to Graduate Study [PDF] on the MechE website). Students must also take at least one graduate mathematics subject (12 units) offered by MIT's Mathematics Department. For the Master of Science in Oceanographic Engineering, see also the requirements listed under the Joint Program with Woods Hole Oceanographic Institution.

The required thesis is an original work of research, development, or design, conducted under the supervision of a faculty or senior research staff member. The thesis usually takes between one and two years to complete.

The Master of Engineering in Advanced Manufacturing and Design is a 12-month professional degree in mechanical engineering that is intended to prepare the student to assume a role of technical leadership in the manufacturing industries. The degree is aimed at practitioners who will use this knowledge to become leaders in existing, as well emerging, manufacturing companies. To qualify for this degree, a student must complete a highly integrated set of subjects and projects that cover the process, product, system, and business aspects of manufacturing, totaling 90 units, plus complete a group-based thesis project with a manufacturing industry. While centered in engineering and firmly grounded in the engineering sciences, this degree program considers the entire enterprise of manufacturing. Students will gain both a broad understanding of the many facets of manufacturing and a knowledge of manufacturing fundamentals from which to build new technologies and businesses. The admission process is identical to that of the Master of Science degree, with the exception that two additional essay questions are required.

Learners who earn an MITx Principles of Manufacturing MicroMasters Credential may apply to the Advanced Manufacturing and Design program and, upon acceptance, would be credited 48 units of advanced standing credit (equivalent to approximately one-third of the full degree program and one semester on campus).

The Mechanical Engineer's degree provides an opportunity for further study beyond the master's level for those who wish to enter engineering practice rather than research. This degree emphasizes breadth of knowledge in mechanical engineering and its economic and social implications, and is quite distinct from the PhD, which emphasizes depth and originality of research.

The engineer's degree requires a broad program of advanced coursework in mechanical engineering totaling at least 162 credit units (typically about 14 subjects), including those taken during the master's degree program. The engineer's degree program is centered around the application of engineering principles to advanced engineering problems and includes a Mechanical Engineering examination and an applications-oriented thesis, which may be an extension of a suitable master's thesis. An engineer's degree typically requires at least one year of study beyond the master's degree.

The Naval Construction and Engineering (NVE) program provides US Navy and US Coast Guard officers, foreign naval officers, and civilian students interested in ships and ship design a broad graduate-level education for a career as a naval engineer.

The program leads to the Naval Engineer's degree, which requires a higher level of professional competence and broader range of knowledge than is required for the degree of Master of Science in Naval Architecture and Marine Engineering or Ocean Engineering. Subjects in the areas of economics, industrial management, and public policy and law, and at least 12 units of comprehensive design are required, in addition to an in-depth curriculum that includes naval architecture, hydrodynamics, ship structures, materials science, and power and propulsion. The program is appropriate for naval officers and civilians who plan to participate in the design and construction of naval ships, as well as those interested in commercial ship design.

For students working toward a simultaneous Naval Engineer's degree and a master's degree, a single thesis is generally acceptable, provided it is appropriate to the specifications of both degrees, demonstrating an educational maturity expected of the Naval Engineer's degree.

The highest academic degree is the Doctor of Science, or Doctor of Philosophy (the two differ only in name). This degree is awarded upon the completion of a program of advanced study, and the performance of significant original research, design, or development. Doctoral degrees are offered in all areas represented by the department's faculty.

Students become candidates for the doctorate by passing the doctoral qualifying examinations. The doctoral program includes a major program of advanced study in the student's principal area of interest, and a minor program of study in a different field. The MechE Graduate Office should be consulted about the deadline for passing the qualifying exam.

The principal component of the program is the thesis. The thesis is a major, original work that makes a significant research, development, or design contribution in its field. The thesis and the program of study are done under a faculty supervisor and a doctoral committee selected by the student and his or her supervisor, and perhaps other interested faculty members. The committee makes an annual examination of the candidate's progress and makes a final recommendation for a public defense of the work. The doctoral program typically requires three years of work beyond the master's degree, although this time is strongly topic dependent.

Interdisciplinary Programs

Graduate students registered in the Department of Mechanical Engineering may elect to participate in interdisciplinary programs of study.

The  Master of Science in Computational Science and Engineering (CSE SM)  is an interdisciplinary program for students interested in the development, analysis, and application of computational approaches to science and engineering. The curriculum is designed with a common core serving all science and engineering disciplines and an elective component focusing on specific disciplinary topics. Students may pursue the CSE SM as a standalone degree or as leading to the CSE PhD program described below.

The Interdisciplinary Doctoral Program in Computational Science and Engineering (CSE PhD) allows students to specialize at the doctoral level in a computation-related field of their choice through focused coursework and a thesis through one of the participating host departments in the School of Engineering or School of Science. The program is administered jointly by the Center for Computational Science and Engineering (CCSE) and the host departments; the emphasis of thesis research activities is the development of new computational methods and/or the innovative application of computational techniques to important problems in engineering and science.

For more information, see the program descriptions under Interdisciplinary Graduate Programs.

Joint Program with the Woods Hole Oceanographic Institution

The Joint Program with the Woods Hole Oceanographic Institution (WHOI)  is intended for students whose primary career objective is oceanography or oceanographic engineering. Students divide their academic and research efforts between the campuses of MIT and WHOI. Joint Program students are assigned an MIT faculty member as academic advisor; thesis research may be supervised by MIT or WHOI faculty. While in residence at MIT, students follow a program similar to that of other students in their home department. The program is described in more detail under Interdisciplinary Graduate Programs.

The 24-month Leaders for Global Operations (LGO)  program  combines graduate degrees in engineering and management for those with previous postgraduate work experience and strong undergraduate degrees in a technical field . During the two-year program, students complete a six-month internship  at one of LGO's partner companies, where  they conduct  research that  forms the basis of a dual-degree thesis. Students finish the program with two MIT degrees: an MBA (or SM in management) and an SM from one of seven engineering programs, some of which have optional or required LGO tracks.  After graduation, alumni  lead strategic initiatives in high-tech, operations, and manufacturing companies.

The Program in Polymers and Soft Matter (PPSM)  offers students from participating departments an interdisciplinary core curriculum in polymer science and engineering, exposure to the broader polymer community through seminars, contact with visitors from industry and academia, and interdepartmental collaboration while working towards a PhD or ScD degree.

Research opportunities include functional polymers, controlled drug delivery, nanostructured polymers, polymers at interfaces, biomaterials, molecular modeling, polymer synthesis, biomimetic materials, polymer mechanics and rheology, self-assembly, and polymers in energy. The program is described in more detail under Interdisciplinary Graduate Programs.

The Master of Science in Technology and Policy is an engineering research degree with a strong focus on the role of technology in policy analysis and formulation. The Technology and Policy Program (TPP) curriculum provides a solid grounding in technology and policy by combining advanced subjects in the student's chosen technical field with courses in economics, politics, quantitative methods, and social science. Many students combine TPP's curriculum with complementary subjects to obtain dual degrees in TPP and either a specialized branch of engineering or an applied social science such as political science or urban studies and planning. See the program description under the Institute for Data, Systems, and Society.

Financial Support

The Department of Mechanical Engineering offers three types of financial assistance to graduate students: research assistantships, teaching assistantships, and fellowships.

The majority of students in the department are supported by research assistantships (RAs), which are appointments to work on particular research projects with particular faculty members. Faculty members procure research grants for various projects and hire graduate students to carry out the research. The research is almost invariably structured so that it becomes the student's thesis. An RA appointment provides a full-tuition scholarship (i.e., covers all tuition) plus a salary that is adequate for a single person. The financial details are outlined in a separate handout available from the MechE Graduate Office. An RA may register for a maximum of 24 units (about two subjects) of classroom subjects per regular term and 12 units in the summer term, and must do at least the equivalent of 24 units of thesis (i.e., research on the project) per term. (Please note that Master of Engineering in Manufacturing students are not eligible for RA or TA positions since their subject credits exceed these limits.)

Teaching assistants (TAs) are appointed to work on specific subjects of instruction. As the name implies, they usually assist a faculty member in teaching, often grading homework problems and tutoring students. In the Mechanical Engineering Department, TAs are very seldom used for regular full-time classroom teaching. Full-time TAs are limited to 24 units of credit per regular term, including both classroom subjects and thesis. The TA appointment does not usually extend through the summer.

A fellowship provides the student with a direct grant, and leaves the student open to select his or her own research project and supervisor. A limited number of awards and scholarships are available to graduate students directly through the department. A number of students are also supported by fellowships from outside agencies, such as the National Science Foundation, Office of Naval Research, and Department of Defense. Scholarships are awarded each year by the Society of Naval Architects and Marine Engineers. These awards are normally granted to applicants whose interest is focused on naval architecture and marine engineering or on ocean engineering. Applications are made directly to the granting agency, and inquiries for the fall term should be made in the preceding fall term.

Prospective students are invited to communicate with the Department regarding any of these educational and financial opportunities.

Experience has shown that the optimum graduate program consists of about equal measures of coursework and research, consistent with an RA appointment. The main advantage of a fellowship is a greater freedom in choosing a research project and supervisor. A teaching assistantship gives the student teaching experience and can also be extremely valuable for reviewing basic subject material—for example, in preparation for the doctoral qualifying exams. It does not, however, leave much time for thesis research and may extend the time that the student needs to complete his or her degree.

For additional information on mechanical engineering graduate admissions, contact Una Sheehan. For general inquiries on the mechanical engineering graduate program, contact Leslie Regan. All can be reached in the MechE Graduate Office , Room 1-112, 617-253-2291.

Research Laboratories and Programs

The Mechanical Engineering Department is organized into seven areas that collectively capture the broad range of interests and activities within it. These areas are:

• Mechanics: Modeling, Experimentation, and Computation (MMEC)

Design, Manufacturing, and Product Development

Controls, instrumentation, and robotics, energy science and engineering, ocean science and engineering, bioengineering, nano/micro science and technology.

The educational opportunities offered to students in mechanical engineering are enhanced by the availability of a wide variety of research laboratories and programs, and well-equipped shops and computer facilities.

The department provides many opportunities for undergraduates to establish a close relationship with faculty members and their research groups. Students interested in project work are encouraged to consult their faculty advisor or approach other members of the faculty.

Many members of the Department of Mechanical Engineering participate in interdepartmental or school-wide research activities. These include the Center for Biomedical Engineering, Center for Computational Science and Engineering, Computational and Systems Biology Program, Computer Science and Artificial Intelligence Laboratory, Institute for Soldier Nanotechnologies, Laboratory for Manufacturing and Productivity, Materials Research Science and Engineering Center, MIT Energy Initiative, Operations Research Center, Program in Polymers and Soft Matter, and Sea Grant College Program. Detailed information about many of these can be found under Research and Study and Interdisciplinary Graduate Programs. The department also hosts a number of industrial consortia, which support some laboratories and research projects. Research in the department is supported, in addition, by a broad range of federal agencies and foundations.

A partial list of departmental laboratories, listed according to the seven core areas of research, follows.

Mechanics: Modeling, Experimentation, and Computation

Amp mechanical behavior of materials laboratory.

Mechanisms of deformation and fracture processes in engineering materials.

Center for Nonlinear Science

Interdisciplinary research into nonlinear phenomena. Incorporates the Nonlinear Dynamical Systems Lab (modeling, simulation, analysis), Nonlinear Dynamics Lab (experiments), and Nonlinear Systems Lab.

Composite Materials and Nondestructive Evaluation Laboratory

Development of quantitative nondestructive evaluation characterizations which are directly correlatable with the mechanical properties of materials and structures.

Finite Element Research Group

Computational procedures for the solution of problems in structural, solid, and fluid mechanics.

Hatsopoulos Microfluids Laboratory

Fundamental research on the behavior of complex fluid systems at microscopic scales, and associated engineering applications.

Auto-ID Laboratory

Creation of the "Internet of Things" using radio frequency identification and wireless sensor networks, and of a global system for tracking goods using a single numbering system called the Electronic Product Code.

Computer-Aided Design Laboratory

Advancing the state of the art in design methodology and computer-aided design methods.

An interdepartmental laboratory in the School of Engineering. Polymer microfabrication for microfluidic devices, chemical mechanical planarization for the semiconductor industry, precision macro- and micro-scale devices, and novel metrology methods for micro-scale devices. Small-scale fuel cells design, photovoltaic material and process research, and manufacture of photovoltaic panels. Identification technologies such as RFID, wireless sensors, and complex systems. Methods to integrate data and models across global networks. Factory-level manufacturing systems design and control, and supply chain design and management. Environmentally benign manufacturing.

Martin Center for Engineering Design

Design methodology, design of integrated electrical-mechanical systems, prototype development, advanced computer-aided design techniques.

Park Center for Complex Systems

Research to understand complexity, educating students and scholars on complexity, designing complex systems for the benefit of humankind, and disseminating knowledge on complexity to the world at large.

Precision Engineering Laboratory

Fundamental and applied research on all aspects of the design, manufacture, and control of high precision machines ranging from manufacturing machines to precision consumer products.

Precision Systems Design and Manufacturing Laboratory

Modeling, design, and manufacturing methods for nanopositioning equipment, carbon nanotube-based mechanisms and machines, and compliant mechanisms.

d'Arbeloff Laboratory for Information Systems and Technology

Research on mechatronics, home and health automation, interface between hardware and software, and development of sensing technologies.

Field and Space Robotics Laboratory

Fundamental physics of robotic systems for unstructured environments. Development, design, and prototyping of control and planning algorithms for robotic applications, including space exploration, rough terrains, sea systems, and medical devices and systems.

Nonlinear Systems Laboratory

Analysis and control of nonlinear physical systems with emphasis on adaptation and learning in robots.

Center for Energy and Propulsion Research

Innovative science and technology for a sustainable energy future in a carbon-constrained world. Fundamental and applied research in energy conversion and transportation, with applications to low-carbon efficient energy and propulsion systems. Includes several research groups:

• Electrochemical Energy Laboratory . Engineering of advanced materials for lithium batteries, proton exchange membrane and solid oxide fuel cells, and air battery and fuel cell hybrids.
• Reacting Gas Dynamics Laboratory . Fluid flow, chemical reaction, and combustion phenomena associated with energy conversion in propulsion systems, power generation, industrial processes, and fires.
• Sloan Automotive Laboratory . Processes and technology that control the performance, efficiency, and environmental impact of internal combustion engines, their lubrication, and fuel requirements.

Cryogenic Engineering Laboratory

Application of thermodynamics, heat transfer, and mechanical design to cryogenic processes and instrumentation and the operation of a liquid helium facility.

Rohsenow Kendall Heat Transfer Laboratory

Fundamental research in microscale/nanoscale transport, convection, laser/material interaction, and high heat fluxes; applied research in water purification, thermoelectric devices, energy-efficient buildings, and thermal management of electronics.

Center for Ocean Engineering

Provides an enduring ocean engineering identity, giving visibility to the outside world of MIT's commitment to the oceans, and serves as the focus point of ocean-related research at the Institute. Supports the research activities of the MIT-WHOI Joint Program in Oceanographic Engineering and the Naval Construction and Engineering Program. Encompasses the activities of the following research groups and laboratories:

• Autonomous Marine Sensing Lab . Distributed ocean sensing concepts for oceanographic science, national defense, and coastal management and protection. Oceanographic sensing and modeling, sonar system technology, computational underwater acoustics, and marine robotics and communication networking.
• Design Lab . Ship design, offshore structure design, marine robotics, geometric and solid modeling, advanced manufacturing, and shipbuilding. Includes the Center for Environmental Sensing and Modeling.
• Experimental Hydrodynamics Lab . Advanced surface ship, offshore platform, and underwater vehicle design. Development of non-invasive flow measurement and visualization methods.
• Impact and Crashworthiness Laboratory . Industry-oriented fracture testing and prediction technology of advanced high-strength steel sheets for automotive and shipbuilding applications. Includes both quasi-static and high strain rate response and effect of loading history on fracture.
• Experimental and Nonlinear Dynamics Lab . Laboratory experiments to obtain insight into all manner of dynamical phenomena, from micro-scale diffusive processes to global-scale oceanic wave fields. Field studies for ocean-related problems.
• Laboratory for Ship and Platform Flows . Modeling of free surface flows past conventional and high-speed vessels and estimation of their resistance and seakeeping in deep and shallow waters. Analytical and computational techniques.
• Laboratory for Undersea Remote Sensing . Ocean exploration, undersea remote sensing of marine life and geophysical phenomena, wave propagation and scattering theory in remote sensing, statistical estimation and information theory, acoustics and seismics, Europa exploration.
• Marine Hydrodynamics Laboratory (Propeller Tunnel) . A variable-pressure recirculating water tunnel capable of speeds up to 10 m/s. Experiments are performed using state-of-the-art measurement techniques and instrumentation.
• Multidisciplinary Ocean Dynamics and Engineering Laboratory . Complex physical and interdisciplinary oceanic dynamics and processes. Mathematical model and computation methods for ocean predictions, dynamical diagnostics, and for data assimilation and data-model comparisons.
• Ocean Engineering Testing Tank . The tank is 108 feet long, 8.5 feet wide, with an average depth of 4.5 feet. The wave generator can generate harmonic or random waves. The tank also houses several laser flow visualization systems.
• Vortical Flow Research Laboratory . Advanced capabilities for simulation of complex vertical flows. Powerful computer workstations and LINUX clusters, computer-video image conversion, and state-of-the-art flow simulation animation technologies.
• MIT Sea Grant AUV Lab . Dedicated to autonomous underwater vehicles (AUVs), the lab is a leading developer of advanced unmanned marine robots, with applications in oceanography, environmental monitoring, and underwater resource studies. It engages in instrumentation and algorithm development for underwater vehicles performing navigation- and information-intensive tasks. Various vehicle platforms, and fabrication tools and materials are available.

Bioinstrumentation Laboratory

Utilization of biology, optics, mechanics, mathematics, electronics, and chemistry to develop innovative instruments for the analysis of biological processes and new devices for the treatment and diagnosis of disease.

Human and Machine Haptics

Interdisciplinary studies aimed at understanding human haptics, developing machine haptics, and enhancing human-machine interactions in virtual reality and teleoperator systems.

Laboratory for Biomechanics of Cells and Biomolecules

Development of new instruments for the measurement of mechanical properties on the scale of a single cell or single molecule to better understand the interactions between biology and mechanics.

Newman Laboratory for Biomechanics and Human Rehabilitation

Research on bioinstrumentation, neuromuscular control, and technology for diagnosis and remediation of disabilities.

Pappalardo Laboratory for Micro/Nano Engineering

Creation of new engineering knowledge and products on the nano and micro scale through multidomain, multidisciplinary, and multiscale research.

Faculty and Teaching Staff

A. John Hart, PhD

Professor of Mechanical Engineering

Head, Department of Mechanical Engineering

Rohan Abeyaratne, PhD

Quentin Berg (1937) Professor of Mechanical Engineering

Triantaphyllos R. Akylas, PhD

Lallit Anand, PhD

Warren and Townley Rohsenow Professor

H. Harry Asada, PhD

Ford Foundation Professor of Engineering

George Barbastathis, PhD

Klaus-Jürgen Bathe, ScD, PhD

Professor Post-Tenure of Mechanical Engineering

Mark Bathe, PhD

Professor of Biological Engineering

(On leave, spring)

John G. Brisson II, PhD

Tonio Buonassisi, PhD

Professor of Mechanical Engineering and Manufacturing

Gang Chen, PhD

Carl Richard Soderberg Professor in Power Engineering

Wai K. Cheng, PhD

Chryssostomos Chryssostomidis, PhD

Henry L. Doherty Professor in Ocean Science and Engineering

Professor Post-Tenure of Mechanical and Ocean Engineering

Jung-Hoon Chun, PhD

Martin L. Culpepper, PhD

Domitilla Del Vecchio, PhD

George N. Hatsopoulos (1949) Faculty Fellowship in Interdisciplinary Research

Daniel Frey, PhD

(On leave, fall)

Ahmed F. Ghoniem, PhD

Ronald C. Crane (1972) Professor

Lorna Gibson, PhD

Matoula S. Salapatas Professor Post-Tenure of Materials Science and Engineering

Leon R. Glicksman, PhD

Professor Post-Tenure of Building Technology

Stephen C. Graves, PhD

Abraham J. Siegel Professor of Management

Professor of Operations Management and Leaders for Global Operations

Member, Institute for Data, Systems, and Society

Linda G. Griffith, PhD

School of Engineering Professor of Teaching Innovation

Timothy G. Gutowski, PhD

Nicolas Hadjiconstantinou, PhD

David E. Hardt, PhD

Ralph E. and Eloise F. Cross Professor in Manufacturing

Douglas Hart, PhD

Asegun Henry, PhD

Robert N. Noyce Career Development Professor

Neville Hogan, PhD

Sun Jae Professor in Mechanical Engineering

Professor of Brain and Cognitive Sciences

Anette E. Hosoi, PhD

Neil and Jane Pappalardo Professor

Professor of Mathematics

Ian Hunter, PhD

George N. Hatsopoulos Professor in Thermodynamics

Roger Dale Kamm, PhD

Cecil H. Green Distinguished Professor Post-Tenure

Professor Post-Tenure of Biological Engineering

Kenneth N. Kamrin, PhD

Rohit N. Karnik, PhD

Tata Professor

Sang-Gook Kim, PhD

Sangbae Kim, PhD

Robert Langer, ScD

David H. Koch (1962) Institute Professor

Professor of Chemical Engineering

Affiliate Faculty, Institute for Medical Engineering and Science

Steven B. Leeb, PhD

Emanuel Landsman (1958) Professor

Professor of Electrical Engineering

John J. Leonard, PhD

Samuel C. Collins Professor

Professor of Mechanical and Ocean Engineering

Pierre F. J. Lermusiaux, PhD

Nam Pyo Suh Professor

John H. Lienhard, PhD

Abdul Latif Jameel Professor of Water and Food

Seth Lloyd, PhD

Nicholas Makris, PhD

Scott R. Manalis, PhD

David H. Koch Professor in Engineering

Associate Head, Department of Biological Engineering

Gareth H. McKinley, PhD

David M. Parks, PhD

Anthony T. Patera, PhD

Nicholas M. Patrikalakis, PhD

Kawasaki Professor of Engineering

Thomas Peacock, PhD

Emanuel Michael Sachs, PhD

Themistoklis Sapsis, PhD

Sanjay E. Sarma, PhD

Fred Fort Flowers (1941) and Daniel Fort Flowers (1941) Professor

Henrik Schmidt, PhD

Paul D. Sclavounos, PhD

Professor of Mechanical Engineering and Naval Architecture

Warren Seering, PhD

Weber-Shaughness Professor

Yang Shao-Horn, PhD

JR East Professor of Engineering

Professor of Materials Science and Engineering

Alexander H. Slocum, PhD

Walter M. May and A. Hazel May Professor of Mechanical Engineering

Jean-Jacques E. Slotine, PhD

Professor of Information Sciences

Peter T. C. So, PhD

Alexandra H. Techet, PhD

Russell L. Tedrake, PhD

Toyota Professor

Professor of Computer Science and Engineering

Professor of Aeronautics and Astronautics

Michael S. Triantafyllou, ScD

Henry L. and Grace Doherty Professor in Ocean Science and Engineering

David L. Trumper, PhD

J. Kim Vandiver, PhD

Kripa K. Varanasi, PhD

David Robert Wallace, PhD

Evelyn N. Wang, PhD

Ford Professor of Engineering

Tomasz Wierzbicki, PhD

Professor Post-Tenure of Applied Mechanics

James H. Williams Jr, PhD

Professor Post-Tenure of Teaching Excellence

Maria Yang, PhD

Gail E. Kendall Professor of Mechanical Engineering

Ioannis V. Yannas, PhD

Professor of Polymer Science and Engineering

Member, Health Sciences and Technology Faculty

Kamal Youcef-Toumi, ScD

Dick K. P. Yue, PhD

Philip J. Solondz (1948) Professor of Engineering

Xuanhe Zhao, PhD

Professor of Civil and Environmental Engineering

Associate Professors

Irmgard Bischofberger, PhD

Class of 1942 Career Development Chair

Associate Professor of Mechanical Engineering

Cullen R. Buie, PhD

Tal Cohen, PhD

Associate Professor of Civil and Environmental Engineering

Betar Gallant, PhD

Ming Guo, PhD

Jeehwan Kim, PhD

Associate Professor of Materials Science and Engineering

Mathias Kolle, PhD

Stefanie Mueller, PhD

TIBCO Founders Professor

Associate Professor of Electrical Engineering and Computer Science

Ellen Roche, PhD

Latham Family Career Development Professor

Core Faculty, Institute for Medical Engineering and Science

Giovanni Traverso, PhD

Amos Winter, PhD

Assistant Professors

Faez Ahmed, PhD

Assistant Professor of Mechanical Engineering

Navid Azizan, PhD

Edgerton Career Development Professor

Kaitlyn P. Becker, PhD

Henry L. and Grace Doherty Professorship in Ocean Science and Engineering

Sili Deng, PhD

Class of 1954 Career Development Professor

Ashwin Gopinath, PhD

Carlos Portela, PhD

Ritu Raman, PhD

Brit (1961) and Alex (1949) d’Arbeloff Career Development Professor

Vivishek Sudhir, PhD

Loza Tadesse, PhD

Wim van Rees, PhD

Sherrie Wang, PhD

Professors of the Practice

Richard M. Wiesman, PhD

Professor of the Practice of Mechanical Engineering

Associate Professors of the Practice

Douglas Jonart, PhD

Associate Professor of the Practice of Naval Construction and Engineering

Visiting Professors

Nicholas Xuanlai Fang, PhD

Visiting Professor of Mechanical Engineering

Visiting Associate Professors

Alberto Rodriguez, PhD

Visiting Associate Professor of Mechanical Engineering

Senior Lecturers

Daniel Braunstein, PhD

Senior Lecturer in Mechanical Engineering

Stephen Fantone, PhD

Franz Hover, PhD

Barbara Hughey, PhD

Raymond S. McCord, MS, Eng

William Plummer, PhD

Amy Smith, MS, MEng

Simona Socrate, PhD

Abbott Weiss, PhD

Dawn Wendell, PhD

Kevin Cedrone, PhD

Lecturer in Mechanical Engineering

Christina Chase, BA

Harrison Chin, PhD

Benita Comeau, PhD

Kevin DiGenova, PhD

Julio Guerrero, PhD

Victor Hung, BS

Bavand Keshavarz, PhD

John Liu, PhD

Peter Nielsen, PhD

James Douglass Penn, PhD

Nathan Phipps, PhD

Robert Podoloff, PhD

Joshua Ramos, PhD

Michael Wardlaw, MS

Instructors

Rachel Mok, PhD

Instructor of Mechanical Engineering

Technical Instructors

Stephen G. Banzaert, MS

Technical Instructor of Mechanical Engineering

Daniel Gilbert, BA

Pierce Hayward, MS

Tasker Smith, BA

Research Staff

Senior research engineers.

Tian Tian, PhD

Senior Research Engineer of Mechanical Engineering

Senior Research Scientists

Anuradha M. Annaswamy, PhD

Senior Research Scientist of Mechanical Engineering

Lynette A. Jones, PhD

Yuming Liu, PhD

Principal Research Scientists

Brian Anthony, PhD

Principal Research Scientist of Mechanical Engineering

Michael Richard Benjamin, PhD

Svetlana V. Boriskina, PhD

H. Igo Krebs, PhD

Research Associates

Chris Mirabito, PhD

Research Associate of Mechanical Engineering

Yi J. Wang, PhD

Research Engineers

Kelli Hendrickson, ScD

Research Engineer of Mechanical Engineering

Benjamin Judge, PhD

Amanda Stack, PhD

Research Scientists

Moises Alencastre Miranda, PhD

Research Scientist of Mechanical Engineering

Susan Elizabeth Amrose, PhD

Rahul Bhattacharyya, PhD

Michael Bono Jr., PhD

Bachir El Fil, PhD

Micha Feigin-Almon, PhD

Richard Ribon Fletcher, PhD

Kiarash Gordiz, PhD

Patrick Haley, PhD

Nevan Clancy Hanumara, PhD

Stephen Ho, PhD

Nora C. Hogan, PhD

Po-Hsun Huang, PhD

Miguel Jimenez, PhD

Jeon Woong Kang, PhD

George E. Karniadakis, PhD

Hyunseok Kim, PhD

Suhin Kim, PhD

Aaron H. Persad, PhD

Mehdi Pishahang, PhD

Themistocles L. Resvanis, PhD

Santosh Shanbhogue, PhD

Dajiang Suo, PhD

Grgur Tokic, PhD

Jianan Zhang, PhD

Lenan Zhang, PhD

Professors Emeriti

Arthur B. Baggeroer, ScD

Professor Emeritus of Mechanical and Ocean Engineering

Professor Emeritus of Electrical Engineering

Mary C. Boyce, PhD

Ford Foundation Professor Emerita of Engineering

Professor Emerita of Mechanical Engineering

C. Forbes Dewey Jr, PhD

Professor Emeritus of Mechanical Engineering

Professor Emeritus of Biological Engineering

Steven Dubowsky, PhD

Professor Emeritus of Aeronautics and Astronautics

David C. Gossard, PhD

Alan J. Grodzinsky, ScD

John B. Heywood, ScD, PhD

Sun Jae Professor Emeritus of Mechanical Engineering

Henry S. Marcus, DBA

Professor Emeritus of Marine Systems

Chiang C. Mei, PhD

Ford Professor Emeritus of Engineering

Professor Emeritus of Civil and Environmental Engineering

Borivoje Mikić, ScD

John Nicholas Newman, ScD

Professor Emeritus of Mechanical Engineering and Naval Architecture

Carl R. Peterson, ScD

Derek Rowell, PhD

Thomas B. Sheridan, ScD

Professor Emeritus of Engineering and Applied Psychology

Nam P. Suh, PhD

Ralph E. and Eloise F. Cross Professor Emeritus

Neil E. Todreas, PhD

Professor Emeritus of Nuclear Science and Engineering

Gerald L. Wilson, PhD

Vannevar Bush Professor Emeritus

First-Year Introductory Subjects

2.00a designing for the future: earth, sea, and space.

Prereq: Calculus I (GIR) and Physics I (GIR) U (Spring) 3-3-3 units

Student teams formulate and complete space/earth/ocean exploration-based design projects with weekly milestones. Introduces core engineering themes, principles, and modes of thinking. Specialized learning modules enable teams to focus on the knowledge required to complete their projects, such as machine elements, electronics, design process, visualization and communication. Includes exercises in written and oral communication and team building. Examples of projects include surveying a lake for millfoil, from a remote controlled aircraft, and then sending out robotic harvesters to clear the invasive growth; and exploration to search for the evidence of life on a moon of Jupiter, with scientists participating through teleoperation and supervisory control of robots. Enrollment limited; preference to freshmen.

2.00B Toy Product Design

Prereq: None U (Spring) 3-5-1 units

Provides students with an overview of design for entertainment and play, as well as opportunities in creative product design and community service. Students develop ideas for new toys that serve clients in the community, and work in teams with local sponsors and with experienced mentors on a themed toy design project. Students enhance creativity and experience fundamental aspects of the product development process, including determining customer needs, brainstorming, estimation, sketching, sketch modeling, concept development, design aesthetics, detailed design, and prototyping. Includes written, visual, and oral communication. Enrollment limited; preference to freshmen.

D. R. Wallace

2.00C[J] Design for Complex Environmental Issues

Same subject as 1.016[J] , EC.746[J] Prereq: None U (Spring) 3-1-5 units

Working in small teams with real clients, students develop solutions related to the year's Terrascope topic. They have significant autonomy as they follow a full engineering design cycle from client profile through increasingly sophisticated prototypes to final product. Provides opportunities to acquire skills with power tools, workshop practice, design, product testing, and teamwork. Focuses on sustainability and appropriate technology that matches the client's specific situation and constraints. Products are exhibited in the public Bazaar of Ideas and evaluated by an expert panel. Class taught in collaboration with D-Lab and Beaver Works. Limited to first-year students. Open to students outside of Terrascope.

A. W. Epstein, J. Grimm, S. L. Hsu

Core Undergraduate Subjects

2.00 introduction to design.

Prereq: None U (Fall; second half of term) 2-2-2 units

Project-based introduction to product development and engineering design. Emphasizes key elements of the design process, including defining design problems, generating ideas, and building solutions. Presents a range of design techniques to help students think about, evaluate, and communicate designs, from sketching to physical prototyping, as well as other types of modeling. Students work both individually and in teams.

2.000 Explorations in Mechanical Engineering

Prereq: None U (Spring) 2-0-0 units

Broad introduction to the various aspects of mechanical engineering at MIT, including mechanics, design, controls, energy, ocean engineering, bioengineering, and micro/nano engineering through a variety of experiences, including discussions led by faculty, students, and industry experts. Reviews research opportunities and undergraduate major options in Course 2 as well as a variety of career paths pursued by alumni. Subject can count toward the 6-unit discovery-focused credit limit for first year students.

2.001 Mechanics and Materials I

Prereq: Physics I (GIR) ; Coreq: 2.087 or 18.03 U (Fall, Spring) 4-1-7 units. REST

Introduction to statics and the mechanics of deformable solids. Emphasis on the three basic principles of equilibrium, geometric compatibility, and material behavior. Stress and its relation to force and moment; strain and its relation to displacement; linear elasticity with thermal expansion. Failure modes. Application to simple engineering structures such as rods, shafts, beams, and trusses. Application to biomechanics of natural materials and structures.

S. Socrate, M. Culpepper, D. Parks, K. Kamrin

2.002 Mechanics and Materials II

Prereq: Chemistry (GIR) and 2.001 U (Spring) 3-3-6 units

Introduces mechanical behavior of engineering materials, and the use of materials in mechanical design. Emphasizes the fundamentals of mechanical behavior of materials, as well as design with materials. Major topics: elasticity, plasticity, limit analysis, fatigue, fracture, and creep. Materials selection. Laboratory experiments involving projects related to materials in mechanical design. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

L. Anand, K. Kamrin, P. Reis

2.003[J] Dynamics and Control I

Same subject as 1.053[J] Prereq: Physics II (GIR) ; Coreq: 2.087 or 18.03 U (Fall, Spring) 4-1-7 units. REST

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems.

J. K. Vandiver, N. C. Makris, N. M. Patrikalakis, T. Peacock, D. Gossard, K. Turitsyn

2.004 Dynamics and Control II

Prereq: Physics II (GIR) and 2.003[J] U (Fall, Spring) 4-2-6 units

Modeling, analysis, and control of dynamic systems. System modeling: lumped parameter models of mechanical, electrical, and electromechanical systems; interconnection laws; actuators and sensors. Linear systems theory: linear algebra; Laplace transform; transfer functions, time response and frequency response, poles and zeros; block diagrams; solutions via analytical and numerical techniques; stability. Introduction to feedback control: closed-loop response; PID compensation; steady-state characteristics, root-locus design concepts, frequency-domain design concepts. Laboratory experiments and control design projects. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

D. Del Vecchio, D. Trumper

2.005 Thermal-Fluids Engineering I

Prereq: ( Physics II (GIR) , 18.03 , and ( 2.086 , 6.100B , or 18.06 )) or permission of instructor U (Fall, Spring) 5-0-7 units

Integrated development of the fundamental principles of thermodynamics, fluid mechanics, and heat transfer, with applications. Focuses on the first and second laws of thermodynamics, mass conservation, and momentum conservation, for both closed and open systems. Entropy generation and its influence on the performance of engineering systems. Introduction to dimensionless numbers. Introduction to heat transfer: conduction, convection, and radiation. Steady-state and transient conduction. Finned surfaces. The heat equation and the lumped capacitance model. Coupled and uncoupled fluid models. Hydrostatics. Inviscid flow analysis and Bernoulli equation. Navier-Stokes equation and its solutions. Viscous internal flows, head losses, and turbulence. Introduction to pipe flows and Moody chart.

2.006 Thermal-Fluids Engineering II

Prereq: 2.005 U (Fall, Spring) 5-0-7 units

Focuses on the application of the principles of thermodynamics, heat transfer, and fluid mechanics to the design and analysis of engineering systems. Dimensional analysis, similarity, and modeling. Pipe systems: major and minor losses. Laminar and turbulent boundary layers. Boundary layer separation, lift and drag on objects. Heat transfer associated with laminar and turbulent flow of fluids in free and forced convection in channels and over surfaces. Pure substance model. Heat transfer in boiling and condensation. Thermodynamics and fluid mechanics of steady flow components of thermodynamic plants. Heat exchanger design. Power cycles and refrigeration plants. Design of thermodynamic plants. Analyses for alternative energy systems. Multi-mode heat transfer and fluid flow in thermodynamic plants.

 R. Karnik, B. Gallant

2.007 Design and Manufacturing I

Prereq: 2.001 and 2.670 ; Coreq: 2.086 U (Spring) 3-4-5 units

Develops students' competence and self-confidence as design engineers. Emphasis on the creative design process bolstered by application of physical laws. Instruction on how to complete projects on schedule and within budget. Robustness and manufacturability are emphasized. Subject relies on active learning via a major design-and-build project. Lecture topics include idea generation, estimation, concept selection, visual thinking, computer-aided design (CAD), mechanism design, machine elements, basic electronics, technical communication, and ethics. Lab fee. Limited enrollment. Pre-registration required for lab assignment; special sections by lottery only.

S. Kim, A. Winter

2.008 Design and Manufacturing II

Prereq: 2.007 ; or Coreq: 2.017[J] and ( 2.005 or 2.051) U (Fall, Spring) 3-3-6 units. Partial Lab

Integration of design, engineering, and management disciplines and practices for analysis and design of manufacturing enterprises. Emphasis is on the physics and stochastic nature of manufacturing processes and systems, and their effects on quality, rate, cost, and flexibility. Topics include process physics and control, design for manufacturing, and manufacturing systems. Group project requires design and fabrication of parts using mass-production and assembly methods to produce a product in quantity. Six units may be applied to the General Institute Lab Requirement. Satisfies 6 units of Institute Laboratory credit. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

J.-H. Chun, J. Hart, S.G. Kim, J. Liu, W. Seering, D. Wendell

2.009 The Product Engineering Process

Prereq: 2.001 , 2.003[J] , ( 2.005 or 2.051), and ( 2.00B , 2.670 , or 2.678 ) U (Fall) 3-3-9 units

Students develop an understanding of product development phases and experience working in teams to design and construct high-quality product prototypes. Design process learned is placed into a broader development context. Primary goals are to improve ability to reason about design alternatives and apply modeling techniques appropriate for different development phases; understand how to gather and process customer information and transform it into engineering specifications; and use teamwork to resolve the challenges in designing and building a substantive product prototype. Instruction and practice in oral communication provided. Enrollment may be limited due to laboratory capacity; preference to Course 2 seniors.

2.013 Engineering Systems Design

Subject meets with 2.733 Prereq: ( 2.001 , 2.003[J] , ( 2.005 or 2.051), and ( 2.00B , 2.670 , or 2.678 )) or permission of instructor U (Fall) 0-6-6 units

Focuses on the design of engineering systems to satisfy stated performance, stability, and/or control requirements. Emphasizes individual initiative, application of fundamental principles, and the compromises inherent in the engineering design process. Culminates in the design of an engineering system, typically a vehicle or other complex system. Includes instruction and practice in written and oral communication through team presentations, design reviews, and written reports. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

2.014 Engineering Systems Development

Subject meets with 2.734 Prereq: ( 2.001 , 2.003[J] , ( 2.005 or 2.051), and ( 2.00B , 2.670 , or 2.678 )) or permission of instructor U (Spring) 0-6-6 units Can be repeated for credit.

Focuses on implementation and operation of engineering systems. Emphasizes system integration and performance verification using methods of experimental inquiry. Students refine their subsystem designs and the fabrication of working prototypes. Includes experimental analysis of subsystem performance and comparison with physical models of performance and with design goals. Component integration into the full system, with detailed analysis and operation of the complete vehicle in the laboratory and in the field. Includes written and oral reports. Students carry out formal reviews of the overall system design. Instruction and practice in oral and written communication provided. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

2.016 Hydrodynamics

Prereq: 2.005 U (Fall) 3-0-9 units

Covers fundamental principles of fluid mechanics and applications to practical ocean engineering problems. Basic geophysical fluid mechanics, including the effects of salinity, temperature, and density; heat balance in the ocean; large scale flows. Hydrostatics. Linear free surface waves, wave forces on floating and submerged structures. Added mass, lift and drag forces on submerged bodies. Includes final project on current research topics in marine hydrodynamics.

A. H. Techet

2.017[J] Design of Electromechanical Robotic Systems

Same subject as 1.015[J] Prereq: 2.003[J] , 2.016 , and 2.678 ; Coreq: 2.671 U (Spring) 3-3-6 units. Partial Lab

Design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Basic statistics, linear systems, Fourier transforms, random processes, spectra and extreme events with applications in design. Lectures on ethics in engineering practice included. Instruction and practice in oral and written communication provided. Satisfies 6 units of Institute Laboratory credit. Enrollment may be limited due to laboratory capacity.

M. Triantafyllou, M. Sacarny

2.019 Design of Ocean Systems

Prereq: 2.001 , 2.003[J] , and ( 2.005 or 2.016 ) U (Spring) 3-3-6 units

Complete cycle of designing an ocean system using computational design tools for the conceptual and preliminary design stages. Team projects assigned, with each student responsible for a specific subsystem. Lectures cover hydrodynamics; structures; power and thermal aspects of ocean vehicles, environment, materials, and construction for ocean use; generation and evaluation of design alternatives. Focus on innovative design concepts chosen from high-speed ships, submersibles, autonomous vehicles, and floating and submerged deep-water offshore platforms. Lectures on ethics in engineering practice included. Instruction and practice in oral and written communication provided. Enrollment may be limited due to laboratory capacity; preference to Course 2 seniors.

C. Chryssostomidis, M. S. Triantafyllou

2.086 Numerical Computation for Mechanical Engineers

Prereq: Calculus II (GIR) and Physics I (GIR) ; Coreq: 2.087 or 18.03 U (Fall, Spring) 2-2-8 units. REST

Covers elementary programming concepts, including variable types, data structures, and flow control. Provides an introduction to linear algebra and probability. Numerical methods relevant to MechE, including approximation (interpolation, least squares, and statistical regression), integration, solution of linear and nonlinear equations, and ordinary differential equations. Presents deterministic and probabilistic approaches. Uses examples from MechE, particularly from robotics, dynamics, and structural analysis. Assignments require MATLAB programming. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

D. Frey, F. Hover, N. Hadjiconstantinou,

2.087 Engineering Mathematics: Linear Algebra and ODEs

Prereq: Calculus II (GIR) and Physics I (GIR) U (Fall; first half of term) Not offered regularly; consult department 2-0-4 units

Introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Linear systems of equations, existence and uniqueness of solutions, Gaussian elimination. Initial value problems, 1st and 2nd order systems, forward and backward Euler, RK4. Eigenproblems, eigenvalues and eigenvectors, including complex numbers, functions, vectors and matrices.

A. Hosoi, T. Peacock

Dynamics and Acoustics

2.032 dynamics.

Prereq: 2.003[J] G (Fall) 4-0-8 units

Review of momentum principles. Hamilton's principle and Lagrange's equations. Three-dimensional kinematics and dynamics of rigid bodies. Study of steady motions and small deviations therefrom, gyroscopic effects, causes of instability. Free and forced vibrations of lumped-parameter and continuous systems. Nonlinear oscillations and the phase plane. Nonholonomic systems. Introduction to wave propagation in continuous systems.

T. R. Akylas, T. Peacock, N. Hadjiconstantinou

2.033[J] Nonlinear Dynamics and Turbulence

Same subject as 1.686[J] , 18.358[J] Subject meets with 1.068 Prereq: 1.060A Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Spring) 3-2-7 units

See description under subject 1.686[J] .

L. Bourouiba

2.034[J] Nonlinear Dynamics and Waves

Same subject as 1.685[J] , 18.377[J] Prereq: Permission of instructor Acad Year 2023-2024: G (Spring) Acad Year 2024-2025: Not offered 3-0-9 units

A unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems. Nonlinear free and forced vibrations; nonlinear resonances; self-excited oscillations; lock-in phenomena. Nonlinear dispersive and nondispersive waves; resonant wave interactions; propagation of wave pulses and nonlinear Schrodinger equation. Nonlinear long waves and breaking; theory of characteristics; the Korteweg-de Vries equation; solitons and solitary wave interactions. Stability of shear flows. Some topics and applications may vary from year to year.

R. R. Rosales

2.036[J] Nonlinear Dynamics and Chaos

Same subject as 18.385[J] Prereq: 18.03 or 18.032 Acad Year 2023-2024: G (Spring) Acad Year 2024-2025: Not offered 3-0-9 units

See description under subject 18.385[J] .

2.050[J] Nonlinear Dynamics: Chaos

Same subject as 12.006[J] , 18.353[J] Prereq: Physics II (GIR) and ( 18.03 or 18.032 ) U (Fall) 3-0-9 units

See description under subject 12.006[J] .

2.060[J] Structural Dynamics

Same subject as 1.581[J] , 16.221[J] Subject meets with 1.058 Prereq: 18.03 or permission of instructor Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Fall) 3-1-8 units

See description under subject 1.581[J] .

2.062[J] Wave Propagation

Same subject as 1.138[J] , 18.376[J] Prereq: 2.003[J] and 18.075 G (Spring) 3-0-9 units

Theoretical concepts and analysis of wave problems in science and engineering with examples chosen from elasticity, acoustics, geophysics, hydrodynamics, blood flow, nondestructive evaluation, and other applications. Progressive waves, group velocity and dispersion, energy density and transport. Reflection, refraction and transmission of plane waves by an interface. Mode conversion in elastic waves. Rayleigh waves. Waves due to a moving load. Scattering by a two-dimensional obstacle. Reciprocity theorems. Parabolic approximation. Waves on the sea surface. Capillary-gravity waves. Wave resistance. Radiation of surface waves. Internal waves in stratified fluids. Waves in rotating media. Waves in random media.

T. R. Akylas, R. R. Rosales

2.065 Acoustics and Sensing

Subject meets with 2.066 Prereq: 2.003[J] , 6.3000 , 8.03 , or 16.003 U (Spring) 3-0-9 units

Introduces the fundamental concepts of acoustics and sensing with waves. Provides a unified theoretical approach to the physics of image formation through scattering and wave propagation in sensing. The linear and nonlinear acoustic wave equation, sources of sound, including musical instruments. Reflection, refraction, transmission and absorption. Bearing and range estimation by sensor array processing, beamforming, matched filtering, and focusing. Diffraction, bandwidth, ambient noise and reverberation limitations. Scattering from objects, surfaces and volumes by Green's Theorem. Forward scatter, shadows, Babinet's principle, extinction and attenuation. Ray tracing and waveguides in remote sensing. Applications to acoustic, radar, seismic, thermal and optical sensing and exploration. Students taking the graduate version complete additional assignments.

N. C. Makris

2.066 Acoustics and Sensing

Subject meets with 2.065 Prereq: 2.003[J] , 6.3000 , 8.03 , 16.003 , or permission of instructor G (Spring) 3-0-9 units

Introduces the fundamental concepts of acoustics and sensing with waves. Provides a unified theoretical approach to the physics of image formation through scattering and wave propagation in sensing. The linear and nonlinear acoustic wave equation, sources of sound, including musical instruments. Reflection, refraction, transmission and absorption. Bearing and range estimation by sensor array processing, beamforming, matched filtering, and focusing. Diffraction, bandwidth, ambient noise and reverberation limitations. Scattering from objects, surfaces and volumes by Green's Theorem. Forward scatter, shadows, Babinet's principle, extinction and attenuation. Ray tracing and waveguides in remote sensing. Applications to acoustic, radar, seismic, thermal and optical sensing and exploration. Students taking the graduate version of the subject complete additional assignments.

Solid Mechanics and Materials

2.071 mechanics of solid materials.

Prereq: 2.002 G (Spring) 4-0-8 units

Fundamentals of solid mechanics applied to the mechanical behavior of engineering materials. Kinematics of deformation, stress, and balance principles. Isotropic linear elasticity and isotropic linear thermal elasticity. Variational and energy methods. Linear viscoelasticity. Small-strain elastic-plastic deformation. Mechanics of large deformation; nonlinear hyperelastic material behavior. Foundations and methods of deformable-solid mechanics, including relevant applications. Provides base for further study and specialization within solid mechanics, including continuum mechanics, computational mechanics (e.g., finite-element methods), plasticity, fracture mechanics, structural mechanics, and nonlinear behavior of materials.

L. Anand, D. M. Parks

2.072 Mechanics of Continuous Media

Prereq: 2.071 Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Fall) 3-0-9 units

Principles and applications of continuum mechanics. Kinematics of deformation. Thermomechanical conservation laws. Stress and strain measures. Constitutive equations including some examples of their microscopic basis. Solution of some basic problems for various materials as relevant in materials science, fluid dynamics, and structural analysis. Inherently nonlinear phenomena in continuum mechanics. Variational principles.

2.073 Solid Mechanics: Plasticity and Inelastic Deformation

Prereq: 2.071 G (Fall) Not offered regularly; consult department 3-0-9 units

Physical basis of plastic/inelastic deformation of solids; metals, polymers, granular/rock-like materials. Continuum constitutive models for small and large deformation of elastic-(visco)plastic solids. Analytical and numerical solution of selected boundary value problems. Applications to deformation processing of metals.

2.074 Solid Mechanics: Elasticity

Prereq: 2.002 and 18.03 G (Fall) 3-0-9 units

Introduction to the theory and applications of nonlinear and linear elasticity. Strain, stress, and stress-strain relations. Several of the following topics: Spherically and cylindrically symmetric problems. Anisotropic material behavior. Piezoelectric materials. Effective properties of composites. Structural mechanics of beams and plates. Energy methods for structures. Two-dimensional problems. Stress concentration at cavities, concentrated loads, cracks, and dislocations. Variational methods and their applications; introduction to the finite element method. Introduction to wave propagation. 

R. Abeyaratne

2.075 Mechanics of Soft Materials

Prereq: None G (Fall) 3-0-9 units

Covers a number of fundamental topics in the emerging field of soft and active materials, including polymer mechanics and physics, poroelasticity, viscoelasticity, and mechanics of electro-magneto-active and other responsive polymers. Lectures, recitations, and experiments elucidate the basic mechanical and thermodynamic principles underlying soft and active materials. Develops an understanding of the fundamental mechanisms for designing soft materials that possess extraordinary properties, such as stretchable, tough, strong, resilient, adhesive and responsive to external stimuli, from molecular to bulk scales.

2.076[J] Mechanics of Heterogeneous Materials

Same subject as 16.223[J] Prereq: 2.002 , 3.032, 16.20 , or permission of instructor Acad Year 2023-2024: G (Fall) Acad Year 2024-2025: Not offered 3-0-9 units

See description under subject 16.223[J] .

B. L. Wardle, S-G. Kim

2.077 Solid Mechanics: Coupled Theories (New)

Prereq: 2.072 G (Fall) 3-0-9 units

Complex problems in solid mechanics for a wide range of applications require a knowledge of the foundational balance laws of mechanics, thermodynamics, and electrodynamics of continua, together with a knowledge of the structure and properties of the materials which are provided by particular constitutive models for the so-called smart-materials, and the materials used in the many applications that involve thermo-, chemo-, electro- and/or magneto-mechanical coupling. Reviews the basic balance laws and the constitutive equations of the classical coupled theories of thermoelasticity and poroelasticity, and provides an introduction to the nonlinear theories of electroelasticity and magnetoelasticity. Examines the governing coupled partial differential equations and suitable boundary conditions. Discusses numerical solutions of the partial differential equations.

2.080[J] Structural Mechanics

Same subject as 1.573[J] Prereq: 2.002 G (Fall) 4-0-8 units

Applies solid mechanics fundamentals to the analysis of marine, civil, and mechanical structures.  Continuum concepts of stress, deformation, constitutive response and boundary conditions are reviewed in selected examples. The principle of virtual work guides mechanics modeling of slender structural components (e.g., beams; shafts; cables, frames; plates; shells), leading to appropriate simplifying assumptions. Introduction to elastic stability.  Material limits to stress in design. Variational methods for computational structural mechanics analysis.

T. Wierzbicki, D. Parks

2.081[J] Plates and Shells: Static and Dynamic Analysis

Same subject as 16.230[J] Prereq: 2.071 , 2.080[J] , or permission of instructor G (Spring) 3-1-8 units

Stress-strain relations for plate and shell elements. Differential equations of equilibrium. Energy methods and approximate solutions. Bending and buckling of rectangular plates. Post-buckling and ultimate strength of cold formed sections and typical stiffened panels used in aerospace, civil, and mechanical engineering; offshore technology; and ship building. Geometry of curved surfaces. General theory of elastic, axisymmetric shells and their equilibrium equations. Buckling, crushing and bending strength of cylindrical shells with applications. Propagation of 1-D elastic waves in rods, geometrical and material dispersion. Plane, Rayleigh surface, and 3-D waves. 1-D plastic waves. Response of plates and shells to high-intensity loads. Dynamic plasticity and fracture. Application to crashworthiness and impact loading of structures.

2.082 Ship Structural Analysis and Design

Prereq: 2.081[J] and 2.701 G (Spring; second half of term) 3-0-3 units

Design application of analysis developed in 2.081[J] . Ship longitudinal strength and hull primary stresses. Ship structural design concepts. Design limit states including plate bending, column and panel buckling, panel ultimate strength, and plastic analysis. Matrix stiffness, and introduction to finite element analysis. Computer projects on the structural design of a midship module.

R. S. McCord, T. Wierzbicki

Computational Engineering

2.0911[j] computational design and fabrication (new).

Same subject as 6.4420[J] Subject meets with 6.8420 Prereq: Calculus II (GIR) and ( 6.1010 or permission of instructor) U (Spring) 3-0-9 units

See description under subject 6.4420[J] .

2.095 Introduction to Finite Element Methods

Subject meets with 2.098 Prereq: 2.086 or permission of instructor Acad Year 2023-2024: Not offered Acad Year 2024-2025: U (Spring) 3-0-9 units

Ordinary differential equation boundary value problems: 2nd-order, 4th-order spatial operators, eigenproblems. Partial differential equations for scalar fields: elliptic, parabolic, hyperbolic. Strong statement, weak form, minimization principle. Rayleigh-Ritz, Galerkin projection. Numerical interpolation, integration, differentiation, best-fit. Finite element method for spatial discretization in one and two space dimensions: formulation (linear, quadratic approximation), mesh generation, bases and discrete equations, uniform and adaptive refinement, a priori and a posteriori error estimates, sparse solvers, implementation, testing. Finite difference-finite element methods for mixed initial-boundary value problems; nonlinear problems and Newton iteration; linear elasticity. Applications in heat transfer and structural analysis. Assignments require MATLAB coding. Students taking graduate version complete additional work.

2.096[J] Introduction to Modeling and Simulation

Same subject as 6.7300[J] , 16.910[J] Prereq: 18.03 or 18.06 G (Fall) 3-6-3 units

See description under subject 6.7300[J] .

2.097[J] Numerical Methods for Partial Differential Equations

Same subject as 6.7330[J] , 16.920[J] Prereq: 18.03 or 18.06 G (Fall) 3-0-9 units

See description under subject 16.920[J] .

2.098 Introduction to Finite Element Methods

Subject meets with 2.095 Prereq: 2.086 or permission of instructor G (Spring) 3-0-9 units

Ordinary differential equation boundary value problems: 2nd-order, 4th-order spatial operators; eigenproblems. Partial differential equations for scalar fields: elliptic, parabolic, hyperbolic. Strong statement, weak form, minimization principle. Rayleigh-Ritz,  Galerkin projection. Numerical interpolation, integration, differentiation; best-fit. Finite element method for spatial discretization in one and two space dimensions: formulation (linear, quadratic approximation), mesh generation, bases and discrete equations, uniform and adaptive refinement, a priori and a posteriori error estimates, sparse solvers, implementation, testing. Finite difference-finite element methods for mixed initial-boundary value problems; nonlinear problems and Newton iteration; linear elasticity. Applications in heat transfer and structural analysis. Assignments require MATLAB coding. Students taking graduate version complete additional work.

2.099[J] Computational Mechanics of Materials

Same subject as 16.225[J] Prereq: Permission of instructor Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Spring) 3-0-9 units

See description under subject 16.225[J] .

R. Radovitzky

System Dynamics and Control

2.110 information, entropy, and computation.

Prereq: Physics I (GIR) U (Fall) Not offered regularly; consult department 3-0-6 units

Explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include information and computation, digital signals, codes, and compression. Biological representations of information. Logic circuits, computer architectures, and algorithmic information. Noise, probability, and error correction. The concept of entropy applied to channel capacity and to the second law of thermodynamics. Reversible and irreversible operations and the physics of computation. Quantum computation.

P. Penfield, Jr.

2.111[J] Quantum Computation

Same subject as 6.6410[J] , 8.370[J] , 18.435[J] Prereq: 8.05 , 18.06 , 18.700 , 18.701 , or 18.C06[J] G (Fall) 3-0-9 units

See description under subject 18.435[J] .

I. Chuang, A. Harrow, P. Shor

2.12 Introduction to Robotics

Subject meets with 2.120 Prereq: 2.004 U (Spring) 3-2-7 units

Cross-disciplinary studies in robot mechanics and intelligence. Emphasizes physical understanding of robot kinematics and dynamics, differential motion and energy method, design and control of robotic arms and mobile robots, and actuators, drives, and transmission. Second half of course focuses on algorithmic thinking and computation, computer vision and perception, planning and control for manipulation, localization and navigation, machine learning for robotics, and human-robot systems. Weekly laboratories include brushless DC motor control, design and fabrication of robotic arms and vehicles, robot vision and navigation, and programming and system integration using Robot Operating System (ROS). Group term project builds intelligent robots for specific applications of interest. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

2.120 Introduction to Robotics

Subject meets with 2.12 Prereq: 2.004 or permission of instructor G (Spring) 3-2-7 units

Cross-disciplinary studies in robot mechanics and intelligence. Emphasizes physical understanding of robot kinematics and dynamics, differential motion and energy method, design and control of robotic arms and mobile robots, and actuators, drives, and transmission. Second half of course focuses on algorithmic thinking and computation, computer vision and perception, planning and control for manipulation, localization and navigation, machine learning for robotics, and human-robot systems. Weekly laboratories include brushless DC motor control, design and fabrication of robotic arms and vehicles, robot vision and navigation, and programming and system integration using Robot Operating System (ROS). Group term project builds intelligent robots for specific applications of interest. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity.

2.121 Stochastic Systems

Subject meets with 2.122 , 2.22 Prereq: None. Coreq: 2.004 U (Spring) 3-0-9 units

Response of systems to stochastic excitation with design applications. Linear time-invariant systems, convolution, Fourier and Laplace transforms. Probability and statistics. Discrete and continuous random variables, derived distributions. Stochastic processes, auto-correlation. Stationarity and ergodicity, power spectral density. Systems driven by random functions, Wiener-Khinchine theorem.  Sampling and filtering. Short- and long-term statistics, statistics of extremes. Problems from mechanical vibrations and statistical linearization, statistical mechanics, and system prediction/identification. Students taking graduate version complete additional assignments and a short-term project.

N. M. Patrikalakis, T. P. Sapsis, M. S. Triantafyllou

2.122 Stochastic Systems

Subject meets with 2.121 , 2.22 Prereq: 2.004 and 2.087 G (Spring) 4-0-8 units

2.124[J] Robotics: Science and Systems (New)

Same subject as 6.4200[J] , 16.405[J] Prereq: (( 1.00 or 6.100A ) and ( 2.003[J] , 6.1010 , 6.1210 , or 16.06 )) or permission of instructor U (Spring) 2-6-4 units. Institute LAB

See description under subject 6.4200[J] . Enrollment limited.

L. Carlone, S. Karaman, D. Hadfield-Manell, J. Leonard

2.131 Advanced Instrumentation and Measurement

Prereq: Permission of instructor G (Spring) 3-6-3 units

Provides training in advanced instrumentation and measurement techniques. Topics include system level design, fabrication and evaluation with emphasis on systems involving concepts and technology from mechanics, optics, electronics, chemistry and biology. Simulation, modeling and design software. Use of a wide range of instruments/techniques (e.g., scanning electron microscope, dynamic signal/system analyzer, impedance analyzer, laser interferometer) and fabrication/machining methods (e.g., laser micro-machining, stereo lithography, computer controlled turning and machining centers). Theory and practice of both linear and nonlinear system identification techniques. Lab sessions include instruction and group project work. No final exam.

I. W. Hunter

2.14 Analysis and Design of Feedback Control Systems

Subject meets with 2.140 Prereq: 2.004 U (Spring) 3-3-6 units

Develops the fundamentals of feedback control using linear transfer function system models. Analysis in time and frequency domains. Design in the s-plane (root locus) and in the frequency domain (loop shaping). Describing functions for stability of certain non-linear systems. Extension to state variable systems and multivariable control with observers. Discrete and digital hybrid systems and use of z-plane design. Extended design case studies and capstone group projects. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

D. L. Trumper, K. Youcef-Toumi

2.140 Analysis and Design of Feedback Control Systems

Subject meets with 2.14 Prereq: 2.004 or permission of instructor G (Spring) 3-3-6 units

Develops the fundamentals of feedback control using linear transfer function system models. Analysis in time and frequency domains. Design in the s-plane (root locus) and in the frequency domain (loop shaping). Describing functions for stability of certain non-linear systems. Extension to state variable systems and multivariable control with observers. Discrete and digital hybrid systems and use of z-plane design. Extended design case studies and capstone group projects. Student taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity.

D. Rowell, D. L. Trumper, K. Youcef-Toumi

2.141 Modeling and Simulation of Dynamic Systems

Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units

Modeling multidomain engineering systems at a level of detail suitable for design and control system implementation. Network representation, state-space models; multiport energy storage and dissipation, Legendre transforms; nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms; Control-relevant properties. Application examples may include electro-mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission.

2.145 Design of Compliant Mechanisms, Machines and Systems (New)

Subject meets with 2.147 Prereq: 2.003[J] and 2.007 U (Fall) 3-3-6 units

Design, modeling and integration of compliance into systems that enable performance which is impractical to obtain via rigid mechanisms. Includes multiple strategies (pseudo-rigid body, topology synthesis, freedom and constraint topology) to engineer compliant mechanisms for mechanical systems. Emphasis is placed upon the integration of first principles (math/physics/engineering classes) to optimize kinematics, stiffness, energy storage/release, load capacity, efficiency and integration with actuation/sensing. Synthesize concepts, optimize them via computational models and test prototypes. Prototypes integrate multiple engineering sub-disciplines (e.g. mechanics + dynamics or mechanics + energy) and are drawn from biological systems, prosthetics, energy harvesting, precision instrumentation, robotics, space-based systems and others. Students taking graduate version complete additional assignments.

M.  Culpepper

2.147 Design of Compliant Mechanisms, Machines and Systems (New)

Subject meets with 2.145 Prereq: 2.003[J] and 2.007 G (Fall) 3-3-6 units

Design, modeling and integration of compliance into systems that enable performance which is impractical to obtain via rigid mechanisms. Students learn strategies (pseudo-rigid body, topology synthesis, freedom and constraint topology) to engineer compliant mechanisms for mechanical systems. Emphasis is placed upon the integration of first principles (math/physics/engineering classes) to optimize kinematics, stiffness, energy storage/release, load capacity, efficiency and integration with actuation/sensing. Students synthesize concepts, optimize them via computational models and test prototypes. Prototypes integrate multiple engineering sub-disciplines (e.g. mechanics + dynamics or mechanics + energy) and are drawn from biological systems, prosthetics, energy harvesting, precision instrumentation, robotics, space-based systems and others. Students taking graduate version complete additional assignments.

2.151 Advanced System Dynamics and Control

Prereq: 2.004 and ( 2.087 or 18.06 ) G (Fall) 4-0-8 units

Analytical descriptions of state-determined dynamic physical systems; time and frequency domain representations; system characteristics - controllability, observability, stability; linear and nonlinear system responses. Modification of system characteristics using feedback. State observers, Kalman filters. Modeling/performance trade-offs in control system design. Basic optimization tools. Positive systems. Emphasizes applications to physical systems.

J.-J. E. Slotine, K. Youcef-Toumi, N. Hogan

2.152[J] Nonlinear Control

Same subject as 9.110[J] Prereq: 2.151 , 6.7100[J] , 16.31 , or permission of instructor G (Spring) 3-0-9 units

Introduction to nonlinear control and estimation in physical and biological systems. Nonlinear stability theory, Lyapunov analysis, Barbalat's lemma. Feedback linearization, differential flatness, internal dynamics. Sliding surfaces. Adaptive nonlinear control and estimation. Multiresolution bases, nonlinear system identification. Contraction analysis, differential stability theory. Nonlinear observers. Asynchronous distributed computation and learning. Concurrent synchronization, polyrhythms. Monotone nonlinear systems. Emphasizes application to physical systems (robots, aircraft, spacecraft, underwater vehicles, reaction-diffusion processes, machine vision, oscillators, internet), machine learning, computational neuroscience, and systems biology. Includes term projects.

J.-J. E. Slotine

2.153 Adaptive Control and Connections to Machine Learning

Prereq: 2.151 Acad Year 2023-2024: G (Fall) Acad Year 2024-2025: Not offered 3-0-9 units

Lays the foundation of adaptive control, and investigates its interconnections with machine learning. Explores fundamental principles of adaptive control, including parameter estimation, recursive algorithms, stability properties, and conditions for convergence. Studies their relationship with machine learning, including the minimization of a performance error and fast convergence. Discusses robustness and regularization in both fields. Derives conditions of learning and implications of imperfect learning. Examines the trade-off between stability and learning. Focuses throughout the term on dynamic systems and on problems where real-time control is needed. Uses examples from aerospace, propulsion, automotive, and energy systems to elucidate the underlying concepts.

A. Annaswamy

2.154 Maneuvering and Control of Surface and Underwater Vehicles

Prereq: 2.22 G (Fall) 3-0-9 units

Maneuvering motions of surface and underwater vehicles. Derivation of equations of motion, hydrodynamic coefficients. Memory effects. Linear and nonlinear forms of the equations of motion. Control surfaces modeling and design. Engine, propulsor, and transmission systems modeling and simulation during maneuvering. Stability of motion. Principles of multivariable automatic control. Optimal control, Kalman filtering, loop transfer recovery. Term project: applications chosen from autopilots for surface vehicles; towing in open seas; remotely operated vehicles.

M. S. Triantafyllou

2.155 Artificial Intelligence and Machine Learning for Engineering Design (New)

Subject meets with 2.156 Prereq: 2.086 , 6.100A , or permission of instructor U (Fall) 3-0-9 units

Machine learning and artificial intelligence techniques in engineering design applications. Emphasizes state-of-the-art machine learning techniques to design new products or systems or solve complex engineering problems. Lectures cover the theoretical and practical aspects of machine learning and optimization methods. Challenge problems, research paper discussions, and interactive in-class activities are used to highlight the unique challenges of machine learning for design applications. A group term project on students' applications of interest. Basic programming and machine learning familiarity are recommended. Students taking graduate version complete additional assignments. 

2.156 Artificial Intelligence and Machine Learning for Engineering Design (New)

Subject meets with 2.155 Prereq: None G (Fall) 3-0-9 units

Machine learning and artificial intelligence techniques in engineering design applications. Emphasizes state-of-the-art machine learning techniques to design new products or systems or solve complex engineering problems. Lectures cover the theoretical and practical aspects of machine learning and optimization methods. Challenge problems, research paper discussions, and interactive in-class activities are used to highlight the unique challenges of machine learning for design applications. A group term project on students' applications of interest. Basic programming and machine learning familiarity are recommended. Students taking graduate version complete additional assignments.

2.16 Learning Machines

Subject meets with 2.168 Prereq: 2.086 , 18.075 , and ( 6.3700 or 18.05 ) U (Spring) Not offered regularly; consult department 4-0-8 units

Introduces fundamental concepts and encourages open-ended exploration of the increasingly topical intersection between artificial intelligence and the physical sciences. Energy and information, and their respective optimality conditions are used to define supervised and unsupervised learning algorithms; as well as ordinary and partial differential equations. Subsequently, physical systems with complex constitutive relationships are drawn from elasticity, biophysics, fluid mechanics, hydrodynamics, acoustics, and electromagnetics to illustrate how machine learning-inspired optimization can approximate solutions to forward and inverse problems in these domains.

G. Barbastathis

2.160 Identification, Estimation, and Learning

Prereq: 2.151 G (Fall) 3-0-9 units

Provides a broad theoretical basis for system identification, estimation, and learning. Least squares estimation and its convergence properties, Kalman filter and extended Kalman filter, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.

2.165[J] Robotics

Same subject as 9.175[J] Prereq: 2.151 or permission of instructor G (Fall) 3-0-9 units

Introduction to robotics and learning in machines. Kinematics and dynamics of rigid body systems. Adaptive control, system identification, sparse representations. Force control, adaptive visual servoing. Task planning, teleoperation, imitation learning. Navigation. Underactuated systems, approximate optimization and control. Dynamics of learning and optimization in networks. Elements of biological planning and control. Motor primitives, entrainment, active sensing, binding models. Term projects.

J.-J. E. Slotine, H. Asada

2.166 Autonomous Vehicles

Prereq: 6.041B or permission of instructor G (Spring) Not offered regularly; consult department 3-1-8 units

Theory and application of probabilistic techniques for autonomous mobile robotics. Topics include probabilistic state estimation and decision making for mobile robots; stochastic representations of the environment; dynamic models and sensor models for mobile robots; algorithms for mapping and localization; planning and control in the presence of uncertainty; cooperative operation of multiple mobile robots; mobile sensor networks; application to autonomous marine (underwater and floating), ground, and air vehicles. Enrollment limited to 8.

J. J. Leonard

2.168 Learning Machines

Subject meets with 2.16 Prereq: None G (Spring) Not offered regularly; consult department 3-0-9 units

2.171 Analysis and Design of Digital Control Systems

Prereq: 2.14 , 2.151 , or permission of instructor G (Fall) Not offered regularly; consult department 3-3-6 units

A comprehensive introduction to digital control system design, reinforced with hands-on laboratory experiences. Major topics include discrete-time system theory and analytical tools; design of digital control systems via approximation from continuous time; direct discrete-time design; loop-shaping design for performance and robustness; state-space design; observers and state-feedback; quantization and other nonlinear effects; implementation issues. Laboratory experiences and design projects connect theory with practice.

D. L. Trumper

2.174[J] Advancing Mechanics and Materials via Machine Learning

Same subject as 1.121[J] Subject meets with 1.052 Prereq: Permission of instructor G (Spring) 3-0-9 units

See description under subject 1.121[J] .

2.177[J] Designing Virtual Worlds (New)

Same subject as CMS.342[J] Subject meets with 2.178[J] , CMS.942[J] Prereq: None U (Fall, Spring) 3-1-2 units

Three primary areas of focus are: creating new Virtual Reality experiences; mapping the state of emerging tools; and hosting guests - leaders in the VR/XR community, who serve as coaches for projects. Students have significant leeway to customize their own learning environment. As the field is rapidly evolving, each semester focuses on a new aspect of virtual worlds, based on the current state of innovations. Students work in teams of interdisciplinary peers from Berklee College of Music and Harvard University. Students taking graduate version complete additional assignments.

2.178[J] Designing Virtual Worlds (New)

Same subject as CMS.942[J] Subject meets with 2.177[J] , CMS.342[J] Prereq: None G (Fall, Spring) 3-1-2 units

2.18 Biomolecular Feedback Systems

Subject meets with 2.180 Prereq: Biology (GIR) , 18.03 , or permission of instructor G (Spring) 3-0-9 units

Comprehensive introduction to dynamics and control of biomolecular systems with emphasis on design/analysis techniques from control theory. Provides a review of biology concepts, regulation mechanisms, and models. Covers basic enabling technologies, engineering principles for designing biological functions, modular design techniques, and design limitations. Students taking graduate version complete additional assignments.

D. Del Vecchio, R. Weiss

2.180 Biomolecular Feedback Systems

Subject meets with 2.18 Prereq: Biology (GIR) , 18.03 , or permission of instructor U (Spring) 3-0-9 units

D. Del Vecchio

2.183[J] Biomechanics and Neural Control of Movement

Same subject as 9.34[J] Subject meets with 2.184 Prereq: 2.004 or permission of instructor G (Spring) 3-0-9 units

Presents a quantitative description of how biomechanical and neural factors interact in human sensory-motor behavior. Students survey recent literature on how motor behavior is controlled, comparing biological and robotic approaches to similar tasks. Topics may include a review of relevant neural, muscular and skeletal physiology, neural feedback and "equilibrium-point" theories, co-contraction strategies, impedance control, kinematic redundancy, optimization, intermittency, contact tasks and tool use. Students taking graduate version complete additional assignments.

2.184 Biomechanics and Neural Control of Movement

Subject meets with 2.183[J] , 9.34[J] Prereq: 2.004 or permission of instructor Acad Year 2023-2024: Not offered Acad Year 2024-2025: U (Spring) 3-0-9 units

Fluid Mechanics and Combustion

2.20 marine hydrodynamics.

Prereq: 1.060 , 2.006 , 2.016 , or 2.06 G (Fall) 4-1-7 units

The fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering. Transport theorem and conservation principles. Navier-Stokes' equation. Dimensional analysis. Ideal and potential flows. Vorticity and Kelvin's theorem. Hydrodynamic forces in potential flow, D'Alembert's paradox, added-mass, slender-body theory. Viscous-fluid flow, laminar and turbulent boundary layers. Model testing, scaling laws. Application of potential theory to surface waves, energy transport, wave/body forces. Linearized theory of lifting surfaces. Experimental project in the towing tank or propeller tunnel.

D. K. P. Yue

2.22 Design Principles for Ocean Vehicles

Subject meets with 2.121 , 2.122 Prereq: 2.20 G (Spring) 3-1-8 units

Design tools for analysis of linear systems and random processes related to ocean vehicles; description of ocean environment including random waves, ocean wave spectra and their selection; short-term and long-term wave statistics; and ocean currents. Advanced hydrodynamics for design of ocean vehicles and offshore structures, including wave forces on towed and moored structures; inertia vs. drag-dominated flows; vortex induced vibrations (VIV) of offshore structures; ship seakeeping and sensitivity of seakeeping performance. Design exercises in application of principles. Laboratory exercises in seakeeping and VIV at model scale.

2.23 Hydrofoils and Propellers

Prereq: 2.20 and 18.085 Acad Year 2023-2024: G (Spring) Acad Year 2024-2025: Not offered 3-0-9 units

Reviews the theory and design of hydrofoil sections; lifting and thickness problems for sub-cavitating sections and unsteady flow problems. Covers lifting line and lifting surface theory with applications to hydrofoil craft, rudder, control surface, propeller and wind turbine rotor design. Topics include propeller lifting line and lifting surface theory; wake adapted propellers, steady and unsteady propeller thrust and torque; waterjets; performance analysis and design of wind turbine rotors. Presents numerical principles of vortex lattice and lifting surface panel methods. Projects illustrate the development of theoretical and computational methods for lifting, propulsion and wind turbine applications.

P. D. Sclavounos

2.24[J] Seakeeping of Ships and Offshore Energy Systems

Same subject as 1.692[J] Prereq: 2.20 and 18.085 Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Spring) 4-0-8 units

Surface wave theory, conservation laws and boundary conditions, properties of regular surface waves and random ocean waves. Linearized theory of floating body dynamics, kinematic and dynamic free surface conditions, body boundary conditions. Simple harmonic motions. Diffraction and radiation problems, added mass and damping matrices. General reciprocity identities on diffraction and radiation. Ship wave resistance theory, Kelvin wake physics, ship seakeeping in regular and random waves. Discusses point wave energy absorbers, beam sea and head-sea devises, oscillating water column device and Well's turbine. Discusses offshore floating energy systems and their interaction with ambient waves, current and wind, including oil and gas platforms, liquefied natural gas (LNG) vessels and floating wind turbines. Homework drawn from real-world applications.

2.25 Fluid Mechanics

Prereq: 2.006 or 2.06; Coreq: 18.075 or 18.085 G (Fall) 4-0-8 units

Survey of principal concepts and methods of fluid dynamics. Mass conservation, momentum, and energy equations for continua. Navier-Stokes equation for viscous flows. Similarity and dimensional analysis. Lubrication theory. Boundary layers and separation. Circulation and vorticity theorems. Potential flow. Introduction to turbulence. Lift and drag. Surface tension and surface tension driven flows.

A. F. Ghoniem, A. E. Hosoi, G. H. McKinley, A. T. Patera

2.250[J] Fluids and Diseases

Same subject as 1.631[J] , HST.537[J] Subject meets with 1.063 Prereq: None Acad Year 2023-2024: G (Spring) Acad Year 2024-2025: Not offered 3-3-6 units

See description under subject 1.631[J] .

2.26[J] Advanced Fluid Dynamics

Same subject as 1.63[J] Prereq: 18.085 and ( 2.25 or permission of instructor) G (Spring) 4-0-8 units

Fundamentals of fluid dynamics intrinsic to natural physical phenomena and/or engineering processes. Discusses a range of topics and advanced problem-solving techniques. Sample topics include brief review of basic laws of fluid motion, scaling and approximations, creeping flows, boundary layers in high-speed flows, steady and transient, similarity method of solution, buoyancy-driven convection in porous media, dispersion in steady or oscillatory flows, physics and mathematics of linearized instability, effects of shear and stratification. In alternate years, two of the following modules will be offered: I: Geophysical Fluid Dynamics of Coastal Waters, II: Capillary Phenomena, III: Non-Newtonian Fluids, IV: Flagellar Swimming.

T. R. Akylas, G. H. McKinley, R. Stocker

2.28 Fundamentals and Applications of Combustion

Prereq: 2.006 or (2.051 and 2.06) Acad Year 2023-2024: G (Fall) Acad Year 2024-2025: Not offered 3-0-9 units

Fundamentals and modeling of reacting gas dynamics and combustion using analytical and numerical methods. Conservation equations of reacting flows. Multi-species transport, chemical thermodynamics and chemical kinetics. Non-equilibrium flow. Detonation and reacting boundary layers. Ignition, flammability, and extinction. Premixed and diffusion flames. Combustion instabilities. Supersonic combustion. Turbulent combustion. Liquid and solid burning. Fire, safety, and environmental impact. Applications to power and propulsion.

A. F. Ghoniem

2.29 Numerical Fluid Mechanics

Subject meets with 2.290 Prereq: 18.075 and ( 2.006 , 2.016 , 2.06, 2.20 , or 2.25 ) G (Spring) 4-0-8 units

Introduction to numerical methods and MATLAB: errors, condition numbers and roots of equations. Navier-Stokes. Direct and iterative methods for linear systems. Finite differences for elliptic, parabolic and hyperbolic equations. Fourier decomposition, error analysis and stability. High-order and compact finite-differences. Finite volume methods. Time marching methods. Navier-Stokes solvers. Grid generation. Finite volumes on complex geometries. Finite element methods. Spectral methods. Boundary element and panel methods. Turbulent flows. Boundary layers. Lagrangian Coherent Structures. Includes a final research project.  Students taking graduate version complete additional assignments.

P. F. J. Lermusiaux

2.290 Numerical Fluid Mechanics

Subject meets with 2.29 Prereq: 2.005 U (Spring) 4-0-8 units

P. Lermusiaux

2.341[J] Macromolecular Hydrodynamics

Same subject as 10.531[J] Prereq: 2.25 , 10.301 , or permission of instructor G (Spring) 3-0-6 units

Physical phenomena in polymeric liquids undergoing deformation and flow. Kinematics and material functions for complex fluids; techniques of viscometry, rheometry; and linear viscoelastic measurements for polymeric fluids. Generalized Newtonian fluids. Continuum mechnanics, frame invariance, and convected derivatives for finite strain viscoelasticity. Differential and integral constitutive equations for viscoelastic fluids. Analytical solutions to isothermal and non-isothermal flow problems; the roles of non-Newtonian viscosity, linear viscoelasticity, normal stresses, elastic recoil, stress relaxation in processing flows. Introduction to molecular theories for dynamics of polymeric fluids. (Extensive class project and presentation required instead of a final exam).

R. C. Armstrong, G. H. McKinley

MEMS and Nanotechnology

2.37 fundamentals of nanoengineering.

Subject meets with 2.370 Prereq: Permission of instructor G (Spring) 3-0-9 units

Presents the fundamentals of molecular modeling in engineering in the context of nanoscale mechanical engineering applications. Statistical mechanics and its connection to engineering thermodynamics. Molecular origin and limitations of macroscopic descriptions and constitutive relations for equilibrium and non-equilibrium behavior. Introduction to molecular simulation, solid-state physics and electrokinetic phenomena. Discusses molecular approaches to modern nanoscale engineering problems. Graduate students are required to complete additional assignments with stronger analytical content.

N. G. Hadjiconstantinou

2.370 Fundamentals of Nanoengineering

Subject meets with 2.37 Prereq: Chemistry (GIR) and 2.001 U (Spring) 3-0-9 units

2.391[J] Nanostructure Fabrication

Same subject as 6.6600[J] Prereq: 2.710 , 6.2370 , 6.2600[J] , or permission of instructor G (Spring) 4-0-8 units

See description under subject 6.6600[J] .

K. K. Berggren

Thermodynamics

2.42 general thermodynamics.

Prereq: Permission of instructor G (Fall) 3-0-9 units

General foundations of thermodynamics from an entropy point of view, entropy generation and transfer in complex systems. Definitions of work, energy, stable equilibrium, available energy, entropy, thermodynamic potential, and interactions other than work (nonwork, heat, mass transfer). Applications to properties of materials, bulk flow, energy conversion, chemical equilibrium, combustion, and industrial manufacturing.

2.43 Advanced Thermodynamics (New)

Prereq: 2.42 or permission of instructor G (Spring) 4-0-8 units

<p class="xmsolistparagraph">Self-contained concise review of general thermodynamics concepts, multicomponent equilibrium properties, chemical equilibrium, electrochemical potentials, and chemical kinetics, as needed to introduce the methods of nonequilibrium thermodynamics and to provide a unified understanding of phase equilibria, transport and nonequilibrium phenomena useful for future energy and climate engineering technologies. Applications include: second-law efficiencies and methods to allocate primary energy consumptions and CO2 emissions in cogeneration and hybrid power systems, minimum work of separation, maximum work of mixing, osmotic pressure and membrane equilibria, metastable states, spinodal decomposition, Onsager's near-equilibrium reciprocity in thermodiffusive, thermoelectric, and electrokinetic cross effects.

G. P. Beretta

Heat and Mass Transfer

2.500 desalination and water purification.

Prereq: 1.020 , 2.006 , 10.302 , (2.051 and 2.06), or permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

Introduces the fundamental science and technology of desalinating water to overcome water scarcity and ensure sustainable water supplies. Covers basic water chemistry, flash evaporation, reverse osmosis and membrane engineering, electrodialysis, nanofiltration, solar desalination, energy efficiency of desalination systems, fouling and scaling, environmental impacts, and economics of desalination systems. Open to upper-class undergraduates.

J. H. Lienhard, M. Balaban

2.51 Intermediate Heat and Mass Transfer

Prereq: ( 2.005 and 18.03 ) or permission of instructor U (Fall) 3-0-9 units

Covers conduction (governing equations and boundary conditions, steady and unsteady heat transfer, resistance concept); laminar and turbulent convection (forced-convection and natural-convection boundary layers, external flows); radiation (blackbody and graybody exchange, spectral and solar radiation); coupled conduction, convection, radiation problems; synthesis of analytical, computational, and experimental techniques; and mass transfer at low rates, evaporation.

J. H. Lienhard, A. T. Patera, E. N. Wang

2.52[J] Modeling and Approximation of Thermal Processes

Same subject as 4.424[J] Prereq: 2.51 G (Fall) Not offered regularly; consult department 3-0-9 units

Provides instruction on how to model thermal transport processes in typical engineering systems such as those found in manufacturing, machinery, and energy technologies. Successive modules cover basic modeling tactics for particular modes of transport, including steady and unsteady heat conduction, convection, multiphase flow processes, and thermal radiation. Includes a creative design project executed by the students.

L. R. Glicksman

2.55 Advanced Heat and Mass Transfer

Prereq: 2.51 G (Spring) 4-0-8 units

Advanced treatment of fundamental aspects of heat and mass transport. Covers topics such as diffusion kinetics, conservation laws, laminar and turbulent convection, mass transfer including phase change or heterogeneous reactions, and basic thermal radiation. Problems and examples include theory and applications drawn from a spectrum of engineering design and manufacturing problems.

J. H. Lienhard

2.57 Nano-to-Macro Transport Processes

Subject meets with 2.570 Prereq: 2.005 , 2.051, or permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

Parallel treatments of photons, electrons, phonons, and molecules as energy carriers; aiming at a fundamental understanding of descriptive tools for energy and heat transport processes, from nanoscale to macroscale. Topics include energy levels; statistical behavior and internal energy; energy transport in the forms of waves and particles; scattering and heat generation processes; Boltzmann equation and derivation of classical laws; and deviation from classical laws at nanoscale and their appropriate descriptions. Applications in nanotechnology and microtechnology. Students taking the graduate version complete additional assignments.

2.570 Nano-to-Macro Transport Processes

Subject meets with 2.57 Prereq: 2.005 , 2.051, or permission of instructor U (Spring) Not offered regularly; consult department 3-0-9 units

2.58 Radiative Transfer

Prereq: 2.51 , 10.302 , or permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

Principles of thermal radiation and their application to engineering heat and photon transfer problems. Quantum and classical models of radiative properties of materials, electromagnetic wave theory for thermal radiation, radiative transfer in absorbing, emitting, and scattering media, and coherent laser radiation. Applications cover laser-material interactions, imaging, infrared instrumentation, global warming, semiconductor manufacturing, combustion, furnaces, and high temperature processing.

2.59[J] Thermal Hydraulics in Power Technology

Same subject as 10.536[J] , 22.313[J] Prereq: 2.006 , 10.302 , 22.312 , or permission of instructor Acad Year 2023-2024: G (Fall) Acad Year 2024-2025: Not offered 3-2-7 units

See description under subject 22.313[J] .

E. Baglietto, M. Bucci

Energy and Power Systems

2.60[j] fundamentals of advanced energy conversion.

Same subject as 10.390[J] Subject meets with 2.62[J] , 10.392[J] , 22.40[J] Prereq: 2.006 , (2.051 and 2.06), or permission of instructor U (Spring) 4-0-8 units

Fundamentals of thermodynamics, chemistry, and transport applied to energy systems. Analysis of energy conversion and storage in thermal, mechanical, chemical, and electrochemical processes in power and transportation systems, with emphasis on efficiency, performance, and environmental impact. Applications to fuel reforming and alternative fuels, hydrogen, fuel cells and batteries, combustion, catalysis, combined and hybrid power cycles using fossil, nuclear and renewable resources. CO 2 separation and capture. Biomass energy. Students taking graduate version complete additional assignments.

A. F. Ghoniem, W. Green

2.603 Fundamentals of Smart and Resilient Grids

Prereq: 2.003[J] U (Fall) Not offered regularly; consult department 4-0-8 units

Introduces the fundamentals of power system structure, operation and control. Emphasizes the challenges and opportunities for integration of new technologies: photovoltaic, wind, electric storage, demand response, synchrophasor measurements. Introduces the basics of power system modeling and analysis. Presents the basic phenomena of voltage and frequency stability as well technological and regulatory constraints on system operation. Describes both the common and emerging automatic control systems and operator decision-making policies. Relies on a combination of traditional lectures, homework assignments, and group projects. Students taking graduate version complete additional assignments.

K. Turitsyn

2.61 Internal Combustion Engines

Prereq: 2.006 G (Spring) Not offered regularly; consult department 3-1-8 units

Fundamentals of how the design and operation of internal combustion engines affect their performance, efficiency, fuel requirements, and environmental impact. Study of fluid flow, thermodynamics, combustion, heat transfer and friction phenomena, and fuel properties, relevant to engine power, efficiency, and emissions. Examination of design features and operating characteristics of different types of internal combustion engines: spark-ignition, diesel, stratified-charge, and mixed-cycle engines. Engine Laboratory project. For graduate and senior undergraduate students.

W. K. Cheng

2.611 Marine Power and Propulsion

Subject meets with 2.612 Prereq: 2.005 G (Fall) 4-0-8 units

Selection and evaluation of commercial and naval ship power and propulsion systems. Analysis of propulsors, prime mover thermodynamic cycles, propeller-engine matching. Propeller selection, waterjet analysis, review of alternative propulsors; thermodynamic analyses of Rankine, Brayton, Diesel, and Combined cycles, reduction gears and integrated electric drive. Battery operated vehicles, fuel cells. Term project requires analysis of alternatives in propulsion plant design for given physical, performance, and economic constraints. Graduate students complete different assignments and exams.

J. Harbour, M. S. Triantafyllou, R. S. McCord

2.612 Marine Power and Propulsion

Subject meets with 2.611 Prereq: 2.005 U (Fall) 4-0-8 units

2.62[J] Fundamentals of Advanced Energy Conversion

Same subject as 10.392[J] , 22.40[J] Subject meets with 2.60[J] , 10.390[J] Prereq: 2.006 , (2.051 and 2.06), or permission of instructor G (Spring) 4-0-8 units

Fundamentals of thermodynamics, chemistry, and transport applied to energy systems. Analysis of energy conversion and storage in thermal, mechanical, chemical, and electrochemical processes in power and transportation systems, with emphasis on efficiency, performance and environmental impact. Applications to fuel reforming and alternative fuels, hydrogen, fuel cells and batteries, combustion, catalysis, combined and hybrid power cycles using fossil, nuclear and renewable resources. CO 2 separation and capture. Biomass energy. Meets with 2.60[J] when offered concurrently; students taking the graduate version complete additional assignments.

2.625[J] Electrochemical Energy Conversion and Storage: Fundamentals, Materials and Applications

Same subject as 10.625[J] Prereq: 2.005 , 3.046 , 3.53 , 10.40 , (2.051 and 2.06), or permission of instructor G (Fall) Not offered regularly; consult department 4-0-8 units

Fundamental concepts, tools, and applications in electrochemical science and engineering. Introduces thermodynamics, kinetics and transport of electrochemical reactions. Describes how materials structure and properties affect electrochemical behavior of particular applications, for instance in lithium rechargeable batteries, electrochemical capacitors, fuel cells, photo electrochemical cells, and electrolytic cells. Discusses state-of-the-art electrochemical energy technologies for portable electronic devices, hybrid and plug-in vehicles, electrical vehicles. Theoretical and experimental exploration of electrochemical measurement techniques in cell testing, and in bulk and interfacial transport measurements (electronic and ionic resistivity and charge transfer cross the electrode-electrolyte interface).

Y. Shao-Horn

2.626 Fundamentals of Photovoltaics

Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 4-0-8 units

Fundamentals of photoelectric conversion: charge excitation, conduction, separation, and collection. Studies commercial and emerging photovoltaic technologies. Cross-cutting themes include conversion efficiencies, loss mechanisms, characterization, manufacturing, systems, reliability, life-cycle analysis, and risk analysis. Photovoltaic technology evolution in the context of markets, policies, society, and environment. Graduate students complete additional work.

T. Buonassisi

2.627 Fundamentals of Photovoltaics

Prereq: Permission of instructor U (Fall) Not offered regularly; consult department 4-0-8 units

2.630 Interfacial Engineering (New)

Interfacial interactions are ubiquitous in many industries including energy, water, agriculture, medical, transportation, and consumer products. Transport processes are typically limited by interfaces. Addresses how interfacial properties (eg., chemistry, morphology, thermal, electrical) can be engineered for significant efficiency enhancements. Topics include surface tension and wetting phenomena, thermodynamics of interfaces, surface chemistry and morphology, nonwetting, slippery, and superwetting surfaces, charged interfaces and electric double layers, intermolecular forces, Van der Waals and double-layer forces, DLVO theory, electrowetting and electro-osmotic flows, electrochemical bubbles, surfactants, phase transitions, and bio-interfaces. Manufacturing approaches, entrepreneurial efforts to translate technologies to markets, guest lectures and start-up company tours provide real-world exposure.  Anticipated enrollment is 15-20.

K. Varanasi

2.65[J] Sustainable Energy

Same subject as 1.818[J] , 10.391[J] , 11.371[J] , 22.811[J] Subject meets with 2.650[J] , 10.291[J] , 22.081[J] Prereq: Permission of instructor G (Fall) 3-1-8 units

See description under subject 22.811[J] .

M. W. Golay

2.650[J] Introduction to Sustainable Energy

Same subject as 10.291[J] , 22.081[J] Subject meets with 1.818[J] , 2.65[J] , 10.391[J] , 11.371[J] , 22.811[J] Prereq: Permission of instructor U (Fall) 3-1-8 units

See description under subject 22.081[J] . Limited to juniors and seniors.

2.651[J] Introduction to Energy in Global Development

Same subject as EC.711[J] Subject meets with EC.791 Prereq: None U (Spring) 3-2-7 units

See description under subject EC.711[J] . Enrollment limited by lottery; must attend first class session.

D. Sweeney, S. Hsu

2.652[J] Applications of Energy in Global Development

Same subject as EC.712[J] Subject meets with EC.782 Prereq: None U (Fall) 4-0-8 units

See description under subject EC.712[J] . Limited to 20; preference to students who have taken EC.711[J] .

D. Sweeney, Staff

Experimental Engineering

2.670 mechanical engineering tools.

Prereq: None U (Fall, IAP, Spring) 0-1-2 units

Introduces the fundamentals of machine tools use and fabrication techniques. Students work with a variety of machine tools including the bandsaw, milling machine, and lathe. Mechanical Engineering students are advised to take this subject in the first IAP after declaring their major. Enrollment may be limited due to laboratory capacity. Preference to Course 2 majors and minors.

M. Culpepper

2.671 Measurement and Instrumentation

Prereq: Physics II (GIR) , 2.001 , 2.003[J] , and 2.086 U (Fall, Spring) 3-3-6 units. Institute LAB

Introduces fundamental concepts and experimental techniques for observation and measurement of physical variables such as force and motion, liquid and gas properties, physiological parameters, and measurements of light, sound, electrical quantities, and temperature. Emphasizes mathematical techniques including uncertainty analysis and statistics, Fourier analysis, frequency response, and correlation functions. Uses engineering knowledge to select instruments and design experimental methods to obtain and interpret meaningful data. Guided learning during lab experiments promotes independent experiment design and measurements performed outside the lab in the semester-long "Go Forth and Measure" project. Advances students' ability to critically read, evaluate, and extract specific technical meaning from information in a variety of media, and provides extensive instruction and practice in written, graphical, and oral communication. Enrollment limited.

I. W. Hunter, M. Kolle, B. Hughey

2.673[J] Instrumentation and Measurement for Biological Systems

Same subject as 20.309[J] Subject meets with 20.409 Prereq: ( Biology (GIR) , Physics II (GIR) , 6.100B , and 18.03 ) or permission of instructor U (Fall, Spring) 3-6-3 units

See description under subject 20.309[J] . Enrollment limited; preference to Course 20 undergraduates.

P. Blainey, S. Manalis, E. Frank, S. Wasserman, J. Bagnall, E. Boyden, P. So

2.674 Introduction to Micro/Nano Engineering Laboratory

Prereq: Physics II (GIR) or permission of instructor U (Spring) 1-3-2 units Credit cannot also be received for 2.675 , 2.676

Presents concepts, ideas, and enabling tools for nanoengineering through experiential lab modules, which include microfluidics, microelectromechanical systems (MEMS), and nanomaterials and nanoimaging tools such as scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic-force microscopy (AFM). Provides knowledge and experience via building, observing and manipulating micro- and nanoscale structures. Exposes students to fluid, thermal, and dynamic systems at small scales. Enrollment limited; preference to Course 2 and 2-A majors and minors.

N. Fang, S. G. Kim, R. Karnik, M. Kolle, J. Kim

2.675 Micro/Nano Engineering Laboratory

Subject meets with 2.676 Prereq: 2.25 and (6.777 or permission of instructor) G (Fall) 2-3-7 units Credit cannot also be received for 2.674

Covers advanced nanoengineering via practical lab modules in connection with classical fluid dynamics, mechanics, thermodynamics, and material physics. Labs include microfluidic systems, microelectromechanical systems (MEMS), emerging nanomaterials such as graphene, carbon nanotubes (CNTs), and nanoimaging tools. Student teams lead an experimental term project that uses the tools and knowledge acquired through the lab modules and experimental work, and culminates in a report and presentation. Recitations cover idea development, experiment design, planning and execution, and analysis of results pertinent to the project. Enrollment limited.

B. Comeau, J. Kim

2.676 Micro/Nano Engineering Laboratory

Subject meets with 2.675 Prereq: 2.001 , 2.003[J] , 2.671 , and Coreq: ( 2.005 or (2.051 and 2.06)) ; or permission of instructor U (Fall) 2-3-7 units Credit cannot also be received for 2.674

Studies advanced nanoengineering via experiental lab modules with classical fluid dynamics, mechanics, thermodynamics, and materials science. Lab modules include microfluidic systems; microelectromechanical systems (MEMS); emerging nanomaterials, such as graphene and carbon nanotubes (CNTs); and nanoimaging tools. Recitation develops in-depth knowledge and understanding of physical phenomena observed in the lab through quantitative analysis. Students have the option to engage in term projects led by students taking 2.675 . Enrollment limited; preference to Course 2 and 2-OE majors and minors.

2.677 Design and Experimentation for Ocean Engineering

Prereq: 2.00A and 2.086 ; Coreq: 2.016 or permission of instructor U (Fall) Not offered regularly; consult department 0-3-3 units

Design and experimental observation for ocean engineering systems focusing on the fundamentals of ocean wave propagation, ocean wave spectra and wave dispersion, cavitation, added mass, acoustic sound propagation in water, sea loads on offshore structures, design of experiments for ship model testing, fish-like swimming propulsion, propellers, and ocean energy harvesting. Emphasizes fundamentals of data analysis of signals from random environments using Fourier transforms, noise filtering, statistics and error analysis using MATLAB. Students carry out experiential laboratory exercises in various Ocean Engineering laboratories on campus, including short labs and demos, longer exercises with written reports, and a final experimental design project. Enrollment may be limited due to laboratory capacity.

2.678 Electronics for Mechanical Systems

Prereq: Physics II (GIR) U (Fall, Spring) 2-2-2 units

Practical introduction to the fundamentals of electronics in the context of electro-mechanical systems, with emphasis on experimentation and project work in basic electronics. Laboratory exercises include the design and construction of simple electronic devices, such as power supplies, amplifiers, op-amp circuits, switched mode dc-dc converters, and dc motor drivers. Surveys embedded microcontrollers as system elements. Laboratory sessions stress the understanding of electronic circuits at the component level, but also point out the modern approach of system integration using commercial modules and specialized integrated circuits. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

S. Banzaert, J. Leonard, M. Kolle, D. Trumper

2.679 Electronics for Mechanical Systems II

Prereq: 2.086 , 2.678 , and 18.03 U (Spring) 2-3-1 units

Extends the concepts and techniques developed in 2.678 to include complex systems and modeling of real-world elements with a strong emphasis on lab experimentation and independent project work. Topics include sampling theory, energy storage, embedded mobile systems, autonomous navigation, printed circuit board design, system integration, and machine vision. Enrollment may be limited; preference to Course 2 majors.

S. Banzaert, J. Leonard

Oceanographic Engineering and Acoustics

2.680 unmanned marine vehicle autonomy, sensing, and communication.

Prereq: Permission of instructor G (Spring) 2-6-4 units

Focuses on software and algorithms for autonomous decision making (autonomy) by underwater vehicles operating in ocean environments. Discusses how autonomous marine vehicles (UMVs) adapt to the environment for improved sensing performance. Covers sensors for acoustic, biological and chemical sensing and their integration with the autonomy system for environmentally adaptive undersea mapping and observation. Introduces students to the underwater acoustic communication environment and various options for undersea navigation, highlighting their relevance to the operation of collaborative undersea networks for environmental sensing. Labs involve the use of the MOOP-IvP autonomy software for the development of integrated sensing, modeling and control solutions. Solutions modeled in simulation environments and include field tests with small autonomous surface and underwater vehicles operated on the Charles River. Limited enrollment.

H. Schmidt, J. J. Leonard, M. Benjamin

2.681 Environmental Ocean Acoustics

Prereq: 2.066 , 18.075 , or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units

Fundamentals of underwater sound, and its application to mapping and surveillance in an ocean environment. Wave equations for fluid and elastic media. Reflection and transmission of sound at plane interfaces. Wave theory representation of acoustic source radiation and propagation in shallow and deep ocean waveguides. Interaction of underwater sound with elastic waves in the seabed and an Arctic ice cover, including effects of porosity and anisotropy. Numerical modeling of the propagation of underwater sound, including spectral methods, normal mode theory, and the parabolic equation method, for laterally homogeneous and inhomogeneous environments. Doppler effects. Effects of oceanographic variability and fluctuation - spatial and temporal coherence. Generation and propagation of ocean ambient noise. Modeling and simulation of signals and noise in traditional sonar systems, as well as modern, distributed, autonomous acoustic surveillance systems.

2.682 Acoustical Oceanography

Prereq: 2.681 G (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Provides brief overview of what important current research topics are in oceanography (physical, geological, and biological) and how acoustics can be used as a tool to address them. Three typical examples are climate, bottom geology, and marine mammal behavior. Addresses the acoustic inverse problem, reviewing inverse methods (linear and nonlinear) and the combination of acoustical methods with other measurements as an integrated system. Concentrates on specific case studies, taken from current research journals.

J. F. Lynch, Woods Hole Staff

2.683 Marine Bioacoustics and Geoacoustics

Prereq: 2.681 G (Spring) 3-0-9 units Can be repeated for credit.

Both active and passive acoustic methods of measuring marine organisms, the seafloor, and their interactions are reviewed. Acoustic methods of detecting, observing, and quantifying marine biological organisms are described, as are acoustic methods of measuring geological properties of the seafloor, including depth, and surficial and volumetric composition. Interactions are also described, including effects of biological scatterers on geological measurements, and effects of seafloor scattering on measurements of biological scatterers on, in, or immediately above the seafloor. Methods of determining small-scale material properties of organisms and the seafloor are outlined. Operational methods are emphasized, and corresponding measurement theory is described. Case studies are used in illustration. Principles of acoustic-system calibration are elaborated.

K. G. Foote, Woods Hole Staff

2.684 Wave Scattering by Rough Surfaces and Inhomogeneous Media

Prereq: 2.066 or permission of instrctor G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

An advanced-level subject designed to give students a working knowledge of current techniques in this area. Material is presented principally in the context of ocean acoustics, but can be used in other acoustic and electromagnetic applications. Includes fundamentals of wave propagation through, and/or scattering by: random media, extended coherent structures, rough surfaces, and discrete scatterers.

T. K. Stanton, A. C. Lavery, Woods Hole Staff

2.687 Time Series Analysis and System Identification

Prereq: 6.3010 and 18.06 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Covers matched filtering, power spectral (PSD) estimation, and adaptive signal processing / system identification algorithms. Algorithm development is framed as an optimization problem, and optimal and approximate solutions are described. Reviews time-varying systems, first and second moment representations of stochastic processes, and state-space models. Also covers algorithm derivation, performance analysis, and robustness to modeling errors. Algorithms for PSD estimation, the LMS and RLS algorithms, and the Kalman Filter are treated in detail.

J. C. Preisig, Woods Hole Staff

2.688 Principles of Oceanographic Instrument Systems -- Sensors and Measurements

Prereq: 2.671 and 18.075 Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Fall) 3-3-6 units

Introduces theoretical and practical principles of design of oceanographic sensor systems. Transducer characteristics for acoustic, current, temperature, pressure, electric, magnetic, gravity, salinity, velocity, heat flow, and optical devices. Limitations on these devices imposed by ocean environment. Signal conditioning and recording; noise, sensitivity, and sampling limitations; standards. Principles of state-of-the-art systems being used in physical oceanography, geophysics, submersibles, acoustics discussed in lectures by experts in these areas. Day cruises in local waters during which the students will prepare, deploy and analyze observations from standard oceanographic instruments constitute the lab work for this subject.

H. Singh, R. Geyer, A. Michel

2.689[J] Projects in Oceanographic Engineering

Same subject as 1.699[J] Prereq: Permission of instructor G (Fall, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

Projects in oceanographic engineering, carried out under supervision of Woods Hole Oceanographic Institution staff. Given at Woods Hole Oceanographic Institution.

J. Preisig, Woods Hole Staff

2.690 Corrosion in Marine Engineering

Prereq: 3.012 and permission of instructor G (Summer) 3-0-3 units

Introduction to forms of corrosion encountered in marine systems material selection, coatings and protection systems. Case studies and causal analysis developed through student presentations.

J. Page, T. Eagar

Naval Architecture

2.700 principles of naval architecture.

Subject meets with 2.701 Prereq: 2.002 U (Fall) 4-2-6 units

Presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. Introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations. Students taking graduate version complete additional assignments.

R. Bebermeyer, P. D. Sclavounos

2.701 Principles of Naval Architecture

Subject meets with 2.700 Prereq: 2.002 G (Fall) 4-2-6 units

R. Bebermeyer, P. Sclavounuos

2.702 Systems Engineering and Naval Ship Design

Prereq: 2.701 G (Spring) 3-3-6 units

Introduces principles of systems engineering and ship design with an overview of naval ship design and acquisition processes, requirements setting, formulation of a systematic plan, design philosophy and constraints, formal decision making methods, selection criteria, optimization, variant analysis, trade-offs, analysis of ship design trends, risk, and cost analysis. Emphasizes the application of principles through completion of a design exercise and project.

R. Bebermeyer, A. Gillespy

2.703 Principles of Naval Ship Design

Prereq: 2.082 , 2.20 , 2.611 , and 2.702 G (Fall) 4-2-6 units

Covers the design of surface ship platforms for naval applications. Includes topics such as hull form selection and concept design synthesis, topside and general arrangements, weight estimation, and technical feasibility analyses (including strength, stability, seakeeping, and survivability.). Practical exercises involve application of design principles and utilization of advanced computer-aided ship design tools.

J. Harbour, J. Page

2.704 Projects in Naval Ship Conversion Design

Prereq: 2.703 G (IAP, Spring) 1-6-5 units

Focuses on conversion design of a naval ship. A new mission requirement is defined, requiring significant modification to an existing ship. Involves requirements setting, design plan formulation and design philosophy, and employs formal decision-making methods. Technical aspects demonstrate feasibility and desirability. Includes formal written and verbal reports and team projects.

2.705 Projects in New Concept Naval Ship Design

Prereq: 2.704 G (Fall, Spring) Units arranged Can be repeated for credit.

Focus on preliminary design of a new naval ship, fulfilling a given set of mission requirements. Design plan formulation, system level trade-off studies, emphasizes achieving a balanced design and total system integration. Formal written and oral reports. Team projects extend over three terms.

R. Bebermeyer, R. Jonart

2.707 Submarine Structural Acoustics

Prereq: 2.066 G (Spring; first half of term) Not offered regularly; consult department 2-0-4 units

Introduction to the acoustic interaction of submerged structures with the surrounding fluid. Fluid and elastic wave equations. Elastic waves in plates. Radiation and scattering from planar structures as well as curved structures such as spheres and cylinders. Acoustic imaging of structural vibrations. Students can take 2.085 in the second half of term.

2.708 Traditional Naval Architecture Design

Prereq: None G (IAP) Not offered regularly; consult department 2-0-1 units

Week-long intensive introduction to traditional design methods in which students hand draw a lines plan of a N. G. Herreshoff (MIT Class of 1870) design based on hull shape offsets taken from his original design model. After completing the plan, students then carve a wooden half-hull model of the boat design. Covers methods used to develop hull shape analysis data from lines plans. Provides students with instruction in safe hand tool use and how to transfer their lines to 3D in the form of their model. Limited to 15.

K. Hasselbalch, J. Harbour

2.71 Optics

Subject meets with 2.710 Prereq: ( Physics II (GIR) , 2.004 , and 18.03 ) or permission of instructor U (Fall) 3-0-9 units

Introduction to optical science with elementary engineering applications. Geometrical optics: ray-tracing, aberrations, lens design, apertures and stops, radiometry and photometry. Wave optics: basic electrodynamics, polarization, interference, wave-guiding, Fresnel and Fraunhofer diffraction, image formation, resolution, space-bandwidth product. Emphasis on analytical and numerical tools used in optical design. Graduate students are required to complete additional assignments with stronger analytical content, and an advanced design project.

G. Barbastathis, P. T. So

2.710 Optics

Subject meets with 2.71 Prereq: ( Physics II (GIR) , 2.004 , and 18.03 ) or permission of instructor G (Fall) 3-0-9 units

2.715[J] Optical Microscopy and Spectroscopy for Biology and Medicine

Same subject as 20.487[J] Prereq: Permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

Introduces the theory and the design of optical microscopy and its applications in biology and medicine. The course starts from an overview of basic optical principles allowing an understanding of microscopic image formation and common contrast modalities such as dark field, phase, and DIC. Advanced microscopy imaging techniques such as total internal reflection, confocal, and multiphoton will also be discussed. Quantitative analysis of biochemical microenvironment using spectroscopic techniques based on fluorescence, second harmonic, Raman signals will be covered. We will also provide an overview of key image processing techniques for microscopic data.

P. T. So, C. Sheppard

2.717 Optical Engineering

Prereq: 2.710 or permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

Theory and practice of optical methods in engineering and system design. Emphasis on diffraction, statistical optics, holography, and imaging. Provides engineering methodology skills necessary to incorporate optical components in systems serving diverse areas such as precision engineering and metrology, bio-imaging, and computing (sensors, data storage, communication in multi-processor systems). Experimental demonstrations and a design project are included.

P. T. So, G. Barbastathis

2.718 Photonic Materials

Subject meets with 2.719 Prereq: 2.003[J] , 8.03 , 6.2370 , or permission of instructor U (Spring) 3-0-9 units

Provides a review of Maxwell's equations and the Helmholtz wave equation. Optical devices: waveguides and cavities, phase and group velocity, causality, and scattering. Light-matter interaction in bulk, surface, and subwavelength-structured matter. Effective media, dispersion relationships, wavefronts and rays, eikonal description of light propagation, phase singularities. Transformation optics, gradient effective media. Includes description of the experimental tools for realization and measurement of photonic materials and effects. Students taking graduate version complete additional assignments.

G. Barbastathis, N. Fang

2.719 Photonic Materials

Subject meets with 2.718 Prereq: 2.003[J] , 8.03 , 6.2370 , or permission of instructor G (Spring) 3-0-9 units

2.70 FUNdaMENTALS of Precision Product Design

Subject meets with 2.77 Prereq: 2.008 U (Fall) 3-3-6 units

Examines design, selection, and combination of machine elements to produce a robust precision system. Introduces process, philosophy and physics-based principles of design to improve/enable renewable power generation, energy efficiency, and manufacturing productivity. Topics include linkages, power transmission, screws and gears, actuators, structures, joints, bearings, error apportionment, and error budgeting. Considers each topic with respect to its physics of operation, mechanics (strength, deformation, thermal effects) and accuracy, repeatability, and resolution. Includes guest lectures from practicing industry and academic leaders. Students design, build, and test a small benchtop precision machine, such as a heliostat for positioning solar PV panels or a two or three axis machine. Prior to each lecture, students review the pre-recorded detailed topic materials and then converge on what parts of the topic they want covered in extra depth in lecture. Students are assessed on their preparation for and participation in class sessions. Students taking graduate version complete additional assignments. Enrollment limited.

2.77 FUNdaMENTALS of Precision Product Design

Subject meets with 2.70 Prereq: 2.008 G (Fall) 3-3-6 units

2.72 Elements of Mechanical Design

Subject meets with 2.720 Prereq: 2.008 and ( 2.005 or 2.051); Coreq: 2.671 U (Spring) 3-3-6 units

Advanced study of modeling, design, integration, and best practices for use of machine elements, such as bearings, bolts, belts, flexures, and gears. Modeling and analysis is based upon rigorous application of physics, mathematics, and core mechanical engineering principles, which are reinforced via laboratory experiences and a design project in which students model, design, fabricate, and characterize a mechanical system that is relevant to a real-world application. Activities and quizzes are directly related to, and coordinated with, the project deliverables. Develops the ability to synthesize, model and fabricate a design subject to engineering constraints (e.g., cost, time, schedule). Students taking graduate version complete additional assignments. Enrollment limited.

M. L. Culpepper

2.720 Elements of Mechanical Design

Subject meets with 2.72 Prereq: Permission of instructor G (Spring) 3-3-6 units

Advanced study of modeling, design, integration, and best practices for use of machine elements, such as bearings, bolts, belts, flexures, and gears. Modeling and analysis is based upon rigorous application of physics, mathematics, and core mechanical engineering principles, which are reinforced via laboratory experiences and a design project in which students model, design, fabricate, and characterize a mechanical system that is relevant to a real-world application. Activities and quizzes are directly related to, and coordinated with, the project deliverables. Develops the ability to synthesize, model and fabricate a design subject to engineering constraints (e.g., cost, time, schedule). Students taking graduate version complete additional assignments.

2.722[J] D-Lab: Design

Same subject as EC.720[J] Prereq: 2.670 or permission of instructor U (Spring) 3-0-9 units

See description under subject EC.720[J] . Enrollment limited by lottery; must attend first class session.

2.7231[J] Introduction to Design Thinking and Innovation in Engineering

Same subject as 6.9101[J] , 16.6621[J] Prereq: None U (Fall, Spring; first half of term) 2-0-1 units

See description under subject 6.9101[J] . Enrollment limited to 25; priority to first-year students.

2.723A Design Thinking and Innovation Leadership for Engineers

Engineering School-Wide Elective Subject. Offered under: 2.723A , 6.910A , 16.662A Prereq: None U (Fall, Spring; first half of term) 2-0-1 units

See description under subject 6.910A .

2.723B Design Thinking and Innovation Project

Engineering School-Wide Elective Subject. Offered under: 2.723B , 6.910B , 16.662B Prereq: 6.910A U (Fall, Spring; second half of term) 2-0-1 units

See description under subject 6.910B .

2.729[J] D-Lab: Design for Scale

Same subject as EC.729[J] Subject meets with 2.789[J] , EC.797[J] Prereq: None. Coreq: 2.008 ; or permission of instructor U (Fall) 3-2-7 units

See description under subject EC.729[J] .

2.733 Engineering Systems Design

Subject meets with 2.013 Prereq: ( 2.001 , 2.003[J] , ( 2.005 or 2.051), and ( 2.00B , 2.670 , or 2.678 )) or permission of instructor Acad Year 2023-2024: G (Fall) Acad Year 2024-2025: Not offered 0-6-6 units

Focuses on the design of engineering systems to satisfy stated performance, stability, and/or control requirements. Emphasizes individual initiative, application of fundamental principles, and the compromises inherent in the engineering design process. Culminates in the design of an engineering system, typically a vehicle or other complex system. Includes instruction and practice in written and oral communication through team presentation, design reviews, and written reports. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity.

2.734 Engineering Systems Development

Subject meets with 2.014 Prereq: ( 2.001 , 2.003[J] , ( 2.005 or 2.051), and ( 2.00B , 2.670 , or 2.678 )) or permission of instructor G (Spring) 0-6-6 units

Focuses on the implementation and operation of engineering systems. Emphasizes system integration and performance verification using methods of experimental inquiry. Students refine their subsystem designs and the fabrication of working prototypes. Includes experimental analysis of subperformance and comparison with physical models of performance and with design goals. component integration into the full system, with detailed analysis and operation of the complete vehicle in the laboratory and in the field. Includes written and oral reports. Students carry out formal reviews of the overall system design. Instruction and practice in oral and written communication provided. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity.

2.737 Mechatronics

Prereq: 6.2000 and ( 2.14 , 6.3100 , or 16.30 ) Acad Year 2023-2024: G (Fall) Acad Year 2024-2025: Not offered 3-5-4 units

Introduction to designing mechatronic systems, which require integration of the mechanical and electrical engineering disciplines within a unified framework. Significant laboratory-based design experiences form subject's core. Final project. Topics include: low-level interfacing of software with hardware; use of high-level graphical programming tools to implement real-time computation tasks; digital logic; analog interfacing and power amplifiers; measurement and sensing; electromagnetic and optical transducers; control of mechatronic systems. Limited to 20.

2.739[J] Product Design and Development

Same subject as 15.783[J] Prereq: 2.009 , 15.761 , 15.778 , 15.814 , or permission of instructor G (Spring) 3-3-6 units

See description under subject 15.783[J] . Engineering students accepted via lottery based on WebSIS pre-registration.

S. Eppinger, M. C. Yang

2.74 Bio-inspired Robotics

Subject meets with 2.740 Prereq: 2.004 or permission of instructor U (Fall) 3-1-8 units

Interdisciplinary approach to bio-inspired design, with emphasis on principle extraction applicable to various robotics research fields, such as robotics, prosthetics, and human assistive technologies. Focuses on three main components: biomechanics, numerical techniques that allow multi-body dynamics simulation with environmental interaction and optimization, and basic robotics techniques and implementation skills. Students integrate the components into a final robotic system project of their choosing through which they must demonstrate their understanding of dynamics and control and test hypothesized design principles. Students taking graduate version complete additional assignments. Enrollment may be limited due to laboratory capacity.

2.740 Bio-inspired Robotics

Subject meets with 2.74 Prereq: 2.004 or permission of instructor G (Fall) 3-3-6 units

Interdisciplinary approach to bio-inspired design, with emphasis on principle extraction applicable to various robotics research fields, such as robotics, prosthetics, and human assistive technologies. Focuses on three main components: biomechanics, numerical techniques that allow multi-body dynamics simulation with environmental interaction and optimization, and basic robotics techniques and implementation skills. Students integrate the components into a final robotic system project of their choosing through which they must demonstrate their understanding of dynamics and control and test hypothesized design principles. Students taking graduate version complete additional assignments. Enrollment may be limited due to lab capacity.

2.744 Product Design

Prereq: 2.009 G (Spring) Not offered regularly; consult department 3-0-9 units

Project-centered subject addressing transformation of ideas into successful products which are properly matched to the user and the market. Students are asked to take a more complete view of a new product and to gain experience with designs judged on their aesthetics, ease of use, and sensitivities to the realities of the marketplace. Lectures on modern design process, industrial design, visual communication, form-giving, mass production, marketing, and environmentally conscious design.

2.75[J] Medical Device Design

Same subject as 6.4861[J] , HST.552[J] Subject meets with 2.750[J] , 6.4860[J] Prereq: 2.008 , 6.2040 , 6.2050 , 6.2060 , 22.071 , or permission of instructor G (Spring) 3-3-6 units

Provides an intense project-based learning experience around the design of medical devices with foci ranging from mechanical to electro mechanical to electronics. Projects motivated by real-world clinical challenges provided by sponsors and clinicians who also help mentor teams. Covers the design process, project management, and fundamentals of mechanical and electrical circuit and sensor design. Students work in small teams to execute a substantial term project, with emphasis placed upon developing creative designs — via a deterministic design process — that are developed and optimized using analytical techniques. Includes mandatory lab. Instruction and practice in written and oral communication provided. Students taking graduate version complete additional assignments. Enrollment limited.

A. H. Slocum, E. Roche, N. C. Hanumara, G. Traverso, A. Pennes

2.750[J] Medical Device Design

Same subject as 6.4860[J] Subject meets with 2.75[J] , 6.4861[J] , HST.552[J] Prereq: 2.008 , 6.2040 , 6.2050 , 6.2060 , 22.071 , or permission of instructor U (Spring) 3-3-6 units

Provides an intense project-based learning experience around the design of medical devices with foci ranging from mechanical to electro mechanical to electronics. Projects motivated by real-world clinical challenges provided by sponsors and clinicians who also help mentor teams. Covers the design process, project management, and fundamentals of mechanical and electrical circuit and sensor design. Students work in small teams to execute a substantial term project, with emphasis placed upon developing creative designs -- via a deterministic design process -- that are developed and optimized using analytical techniques. Includes mandatory lab. Instruction and practice in written and oral communication provided. Students taking graduate version complete additional assignments. Enrollment limited.

A. H. Slocum, E. Roche, N. C. Hanumara, G. Traverso, A. Pennes

2.752 Development of Mechanical Products

Subject meets with 2.753 Prereq: 2.009 , 2.750[J] , or permission of instructor U (Spring) Not offered regularly; consult department 3-0-9 units

Focuses on evolving a product from proof-of-concept to beta prototype: Includes team building, project planning, budgeting, resource planning; models for scaling, tolerancing and reliability, patents, business planning. Students/teams start with a proof-of-concept product they bring to class or select from projects provided by instructor. In lieu of taking 12 units of 2.THU , Course 2 majors taking 2.752 may write a bachelor's thesis that documents their contributions to the product developed in the team project. Students taking the graduate version complete additional assignments. Enrollment limited; preference to Course 2 majors and minors.

2.753 Development of Mechanical Products

Subject meets with 2.752 Prereq: 2.009 , 2.750[J] , or permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

Focuses on evolving a product from proof-of-concept to beta prototype: Includes team building, project planning, budgeting, resource planning; models for scaling, tolerancing and reliability, patents, business planning. Students/teams start with a proof-of-concept product they bring to class or select from projects provided by instructor. In lieu of taking 12 units of 2.THU , Course 2 majors taking 2.752 may write a bachelor's thesis that documents their contributions to the product developed in the team project. Students taking the graduate version complete additional assignments. Enrollment limited.

2.76 Global Engineering

Subject meets with 2.760 Prereq: 2.008 or permission of instructor G (Fall) 3-0-9 units

Combines rigorous engineering theory and user-centered product design to create technologies for developing and emerging markets. Covers machine design theory to parametrically analyze technologies; bottom-up/top-down design processes; engagement of stakeholders in the design process; socioeconomic factors that affect adoption of products; and developing/emerging market dynamics and their effect on business and technology. Includes guest lectures from subject matter experts in relevant fields and case studies on successful and failed technologies. Student teams apply course material to term-long projects to create new technologies, developed in collaboration with industrial partners and other stakeholders in developing/emerging markets. Students taking graduate version complete additional assignments.

2.760 Global Engineering

Subject meets with 2.76 Prereq: 2.008 or permission of instructor U (Fall) 3-0-9 units

2.771[J] D-Lab: Supply Chains

Same subject as 15.772[J] , EC.733[J] Subject meets with 2.871 Prereq: None U (Spring) Not offered regularly; consult department 3-3-6 units

See description under subject 15.772[J] .

S. C. Graves

2.772[J] Thermodynamics of Biomolecular Systems

Same subject as 20.110[J] Prereq: ( Biology (GIR) , Calculus II (GIR) , Chemistry (GIR) , and Physics I (GIR) ) or permission of instructor U (Fall) 5-0-7 units. REST

See description under subject 20.110[J] .

M. Birnbaum, C. Voigt

2.777 Large and Complex Systems Design and Concept Development

Subject meets with 2.778 Prereq: 2.00B , 2.007 , or permission of instructor U (Fall) 3-0-9 units

Examines structured principles and processes to develop concepts for large and complex systems. Term projects introduce students to large-scale system development with several areas of emphasis, including idea generation, concept development and refinement, system-level thinking, briefing development and presentation, and proposal generation. Interactive lectures and presentations guide students throughout the course to develop and deliver team presentations focused on solving large and complex problems. Includes a semester-long project in which students apply design tools/processes to solve a specific problem. Students taking graduate version complete the project individually.

2.778 Large and Complex Systems Design and Concept Development

Subject meets with 2.777 Prereq: Permission of instructor G (Fall) 3-0-9 units

Examines structured principles and processes to develop concepts for large and complex systems. Term projects introduce students to large-scale system development with several areas of emphasis, including idea generation, concept development and refinement, system-level thinking, briefing development and presentation, and proposal generation. Interactive lectures and presentations guide students throughout the course to develop and deliver individual and team presentations focused on solving large and complex problems. Includes a semester-long project in which students apply design tools/processes to solve a specific problem. Students taking graduate version complete project individually. Limited enrollment.

2.78[J] Principles and Practice of Assistive Technology

Same subject as 6.4530[J] , HST.420[J] Prereq: Permission of instructor U (Fall) Not offered regularly; consult department 2-4-6 units

See description under subject 6.4530[J] . Enrollment may be limited.

R. C. Miller, J. E. Greenberg, J. J. Leonard

2.782[J] Design of Medical Devices and Implants

Same subject as HST.524[J] Prereq: ( Biology (GIR) , Chemistry (GIR) , and Physics I (GIR) ) or permission of instructor G (Spring) 3-0-9 units

Solution of clinical problems by use of implants and other medical devices. Systematic use of cell-matrix control volumes. The role of stress analysis in the design process. Anatomic fit: shape and size of implants. Selection of biomaterials. Instrumentation for surgical implantation procedures. Preclinical testing for safety and efficacy: risk/benefit ratio assessment. Evaluation of clinical performance: design of clinical trials. Project materials drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants.

I. V. Yannas, M. Spector

2.785[J] Cell-Matrix Mechanics

Same subject as HST.523[J] Prereq: ( Biology (GIR) , Chemistry (GIR) , and 2.001 ) or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units

Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine.

2.787[J] Tissue Engineering and Organ Regeneration

Same subject as HST.535[J] Prereq: ( Biology (GIR) , Chemistry (GIR) , and Physics I (GIR) ) or permission of instructor G (Fall) 3-0-9 units

See description under subject HST.535[J] .

M. Spector, I. V. Yannas

2.788 Mechanical Engineering and Design of Living Systems

Prereq: None G (Fall) 4-2-6 units

For students interested in research at the interface of mechanical engineering, biology, and materials science. Specific emphasis lies on interfacing living systems with engineered materials and devices, and on engineering living system behavior.

M. Kolle, M. Guo

2.789[J] D-Lab: Design for Scale

Same subject as EC.797[J] Subject meets with 2.729[J] , EC.729[J] Prereq: None. Coreq: 2.008 ; or permission of instructor G (Fall) 3-2-7 units

See description under subject EC.797[J] .

M. Yang, H. Quintus-Bosz, S. Grama, K. Bergeron

2.79[J] Biomaterials: Tissue Interactions

Same subject as HST.522[J] Prereq: ( Biology (GIR) , Chemistry (GIR) , and Physics I (GIR) ) or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units

Principles of materials science and cell biology underlying the development and implementation of biomaterials for the fabrication of medical devices/implants, including artificial organs and matrices for tissue engineering and regenerative medicine. Employs a conceptual model, the "unit cell process for analysis of the mechanisms underlying wound healing and tissue remodeling following implantation of biomaterials/devices in various organs, including matrix synthesis, degradation, and contraction. Methodology of tissue and organ regeneration. Discusses methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Design of implants and prostheses based on control of biomaterials-tissue interactions. Comparative analysis of intact, biodegradable, and bioreplaceable implants by reference to case studies. Criteria for restoration of physiological function for tissues and organs.

2.791[J] Cellular Neurophysiology and Computing

Same subject as 6.4810[J] , 9.21[J] , 20.370[J] Subject meets with 2.794[J] , 6.4812[J] , 9.021[J] , 20.470[J] , HST.541[J] Prereq: ( Physics II (GIR) , 18.03 , and ( 2.005 , 6.2000 , 6.3000 , 10.301 , or 20.110[J] )) or permission of instructor U (Spring) 5-2-5 units

See description under subject 6.4810[J] . Preference to juniors and seniors.

J. Han, T. Heldt

2.792[J] Quantitative and Clinical Physiology

Same subject as 6.4820[J] , HST.542[J] Subject meets with 2.796[J] , 6.4822[J] Prereq: Physics II (GIR) , 18.03 , or permission of instructor U (Fall) 4-2-6 units

See description under subject 6.4820[J] .

T. Heldt, R. G. Mark

2.793[J] Fields, Forces and Flows in Biological Systems

Same subject as 6.4830[J] , 20.330[J] Prereq: Biology (GIR) , Physics II (GIR) , and 18.03 U (Spring) 4-0-8 units

See description under subject 20.330[J] .

J. Han, S. Manalis

2.794[J] Cellular Neurophysiology and Computing

Same subject as 6.4812[J] , 9.021[J] , 20.470[J] , HST.541[J] Subject meets with 2.791[J] , 6.4810[J] , 9.21[J] , 20.370[J] Prereq: ( Physics II (GIR) , 18.03 , and ( 2.005 , 6.2000 , 6.3000 , 10.301 , or 20.110[J] )) or permission of instructor G (Spring) 5-2-5 units

See description under subject 6.4812[J] .

2.795[J] Fields, Forces, and Flows in Biological Systems

Same subject as 6.4832[J] , 10.539[J] , 20.430[J] Prereq: Permission of instructor G (Fall) 3-0-9 units

See description under subject 20.430[J] .

M. Bathe, A. J. Grodzinsky

2.796[J] Quantitative Physiology: Organ Transport Systems

Same subject as 6.4822[J] Subject meets with 2.792[J] , 6.4820[J] , HST.542[J] Prereq: 6.4810[J] and ( 2.006 or 6.2300 ) G (Fall) 4-2-6 units

See description under subject 6.4822[J] .

2.797[J] Molecular, Cellular, and Tissue Biomechanics

Same subject as 3.053[J] , 6.4840[J] , 20.310[J] Subject meets with 2.798[J] , 3.971[J] , 6.4842[J] , 10.537[J] , 20.410[J] Prereq: Biology (GIR) and 18.03 U (Spring) 4-0-8 units

Develops and applies scaling laws and the methods of continuum mechanics to biomechanical phenomena over a range of length scales. Topics include structure of tissues and the molecular basis for macroscopic properties; chemical and electrical effects on mechanical behavior; cell mechanics, motility and adhesion; biomembranes; biomolecular mechanics and molecular motors. Experimental methods for probing structures at the tissue, cellular, and molecular levels. Students taking graduate version complete additional assignments.

M. Bathe, K. Ribbeck, P. T. So

2.798[J] Molecular, Cellular, and Tissue Biomechanics

Same subject as 3.971[J] , 6.4842[J] , 10.537[J] , 20.410[J] Subject meets with 2.797[J] , 3.053[J] , 6.4840[J] , 20.310[J] Prereq: Biology (GIR) and 18.03 G (Spring) 3-0-9 units

2.799 The Cell as a Machine

Prereq: 5.07[J] , 7.05 , or 18.03 G (Fall) Not offered regularly; consult department 3-3-6 units

Examines a variety of essential cellular functions from the perspective of the cell as a machine. Includes phenomena such as nuclear organization, protein synthesis, cell and membrane mechanics, cell migration, cell cycle control, cell transformation. Lectures are provided by video twice per week; live 3-hour recitation one evening per week. Course is taken simultaneously by students at multiple universities; homework and take-home exams common to all students. Preference to students in Courses 2 and 20.

R. Kamm, M. Sheetz, H. Yu

Manufacturing

2.810 manufacturing processes and systems.

Prereq: 2.001 , 2.006 , and 2.008 G (Fall) 3-3-6 units

Introduction to manufacturing processes and manufacturing systems including assembly, machining, injection molding, casting, thermoforming, and more. Emphasis on the physics and randomness and how they influence quality, rate, cost, and flexibility. Attention to the relationship between the process and the system, and the process and part design. Project (in small groups) requires fabrication (and some design) of a product using several different processes (as listed above). Enrollment may be limited due to laboratory constraints; preference given to MechE students and students who need to satisfy degree requirements.

J. Hart, D. Wendell, W. Seering, J. Liu

2.812 Solving for Carbon Neutrality at MIT

Prereq: None Acad Year 2023-2024: Not offered Acad Year 2024-2025: U (Spring) 3-3-6 units

Working in teams, students address the problem of reducing MIT's greenhouse gas emissions in a manner consistent with the climate goals of maintaining our planet in a suitable regime to support human society and the environment. Solution scenarios include short-, middle- and long-term strategies. Experts from MIT's faculty and operations staff, as well as outside experts who address the multidisciplinary features of the problem guide solutions. These include climate science, ethics, carbon accounting, cost estimating, MIT's energy supply, energy demand, and infrastructure, new technologies, financial instruments, electricity markets, policy, human behavior, and regulation.Develops skills to address carbon neutrality at other universities, and at other scales, including cities and nations. Students taking graduate version complete additional assignments.

T. Gutowski, J. Newman

2.813 Energy, Materials, and Manufacturing

Subject meets with 2.83 Prereq: 2.008 or permission of instructor Acad Year 2023-2024: U (Spring) Acad Year 2024-2025: Not offered 3-0-9 units

Introduction to the major dilemma that faces manufacturing and society for the 21st century: how to support economic development while protecting the environment. Subject addresses industrial ecology, materials flows, life-cycle analysis, thermodynamic analysis and exergy accounting, manufacturing process performance, product design analysis, design for the environment, recycling and ecological economics. Combines lectures and group discussions of journal articles and selected literature, often with opposing views. Graduate students complete term-long project with report required for graduate credit.

T. G. Gutowski

2.814 Exploring Sustainability at Different Scales (New)

Subject meets with 1.834[J] , 2.834[J] Prereq: None U (Fall) 3-0-9 units

Develops environmental accounting tools including energy, carbon, materials, land use, and possibly others, from small scales (e.g., products and processes) to larger scales, (e.g., companies, nations and global) to reveal how reoccurring human behavior patterns have dominated environmental outcomes. Involves visiting experts and readings in areas such as ethics, economics, governance, and development to frame core issues in human relationship to the environment and future societies. Explores how local actions, including engineering interventions and behavior change, play out at larger scales associated with the concept of sustainability, and how local actions may be modified to realize sustainability. Class is participatory and includes an exploratory project. Students taking graduate version complete additional assignments. Limited to 25.

T. Gutowski

2.821[J] Structural Materials

Same subject as 3.371[J] Prereq: Permission of instructor G (Fall, Summer) 3-0-9 units Can be repeated for credit. Credit cannot also be received for 3.171

See description under subject 3.371[J] .

D. Baskin, A. Slocum

2.83 Energy, Materials and Manufacturing

Subject meets with 2.813 Prereq: 2.008 or permission of instructor Acad Year 2023-2024: G (Spring) Acad Year 2024-2025: Not offered 3-0-9 units

2.830[J] Control of Manufacturing Processes

Same subject as 6.6630[J] Prereq: 2.008 , 6.2600[J] , or 6.3700 G (Fall) 3-0-9 units

Statistical modeling and control in manufacturing processes. Use of experimental design and response surface modeling to understand manufacturing process physics. Defect and parametric yield modeling and optimization. Forms of process control, including statistical process control, run by run and adaptive control, and real-time feedback control. Application contexts include semiconductor manufacturing, conventional metal and polymer processing, and emerging micro-nano manufacturing processes.

D. E. Hardt, D. S. Boning

2.832 Solving for Carbon Neutrality at MIT

Prereq: None Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Spring) 3-3-6 units

2.834[J] Exploring Sustainability at Different Scales (New)

Same subject as 1.834[J] Subject meets with 2.814 Prereq: None G (Fall) 3-0-9 units

2.851[J] System Optimization and Analysis for Operations

Same subject as 15.066[J] Prereq: Calculus II (GIR) G (Summer) 4-0-8 units

See description under subject 15.066[J] . Restricted to Leaders for Global Operations students.

2.853 Introduction to Manufacturing Systems

Subject meets with 2.854 Prereq: 2.008 U (Fall) 3-0-9 units

Provides ways to analyze manufacturing systems in terms of material flow and storage, information flow, capacities, and times and durations of events. Fundamental topics include probability, inventory and queuing models, forecasting, optimization, process analysis, and linear and dynamic systems. Factory planning and scheduling topics include flow planning, bottleneck characterization, buffer and batch-size tactics, seasonal planning, and dynamic behavior of production systems. Graduate students are required to complete additional assignments with stronger analytical content.

S. B. Gershwin

2.854 Introduction to Manufacturing Systems

Subject meets with 2.853 Prereq: Undergraduate mathematics G (Fall) 3-0-9 units

Provides ways to analyze manufacturing systems in terms of material flow and storage, information flow, capacities, and times and durations of events. Fundamental topics include probability, inventory and queuing models, forecasting, optimization, process analysis, and linear and dynamic systems. Factory planning and scheduling topics include flow planning, bottleneck characterization, buffer and batch-size tactics, seasonal planning, and dynamic behavior of production systems. Graduate students are required to complete additional assignments.

2.871 D-Lab: Supply Chains

Subject meets with 2.771[J] , 15.772[J] , EC.733[J] Prereq: None G (Spring) Not offered regularly; consult department 3-3-6 units

Introduces concepts of supply chain design and planning with a focus on supply chains for products destined to improve quality of life in developing countries. Topics include demand estimation, process analysis and improvement, facility location and capacity planning, inventory management, and supply chain coordination. Also covers issues specific to emerging markets, such as sustainable supply chains, choice of distribution channels, and how to account for the value-adding role of a supply chain. Students conduct D-Lab-based projects on supply chain design or improvement. Students taking graduate version will complete additional assignments.

2.874[J] Process Data Analytics

Same subject as 10.354[J] Subject meets with 2.884[J] , 10.554[J] Prereq: 18.03 or permission of instructor Acad Year 2023-2024: Not offered Acad Year 2024-2025: U (Fall) 4-0-8 units

See description under subject 10.354[J] .

R. D. Braatz, B. Anthony

2.884[J] Process Data Analytics

Same subject as 10.554[J] Subject meets with 2.874[J] , 10.354[J] Prereq: None Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Fall) 4-0-8 units

See description under subject 10.554[J] .

2.888 Professional Seminar in Global Manufacturing Innovation and Entrepreneurship

Prereq: None G (Spring) 2-0-1 units

Covers a broad range of topics in modern manufacturing, from models and structures for 21st-century operations, to case studies in leadership from the shop floor to the executive office. Also includes global perspectives from Asia, Europe and North America, with guest speakers from all three regions. Explores opportunities for new ventures in manufacturing. Intended primarily for Master of Engineering in Manufacturing students.

D. E. Hardt, S. B. Gershwin

2.890[J] Global Operations Leadership Seminar

Same subject as 10.792[J] , 15.792[J] , 16.985[J] Prereq: None G (Fall, Spring) 2-0-0 units Can be repeated for credit.

See description under subject 15.792[J] . Preference to LGO students.

Engineering Management

2.351[j] introduction to making and hardware ventures.

Same subject as 15.351[J] Prereq: Permission of instructor G (Spring) 3-0-3 units

See description under subject 15.351[J] . Enrollment limited; application required.

C. Lowell, M. Kenney, M. Culpepper

2.900 Ethics for Engineers

Engineering School-Wide Elective Subject. Offered under: 1.082 , 2.900 , 6.9320 , 10.01 , 16.676 , 22.014 Subject meets with 6.9321 , 20.005 Prereq: None U (Fall, Spring) 2-0-4 units

See description under subject 10.01 .

D. A. Lauffenberger, B. L. Trout

2.907[J] Innovation Teams

Same subject as 10.807[J] , 15.371[J] Prereq: None G (Fall) 4-4-4 units

See description under subject 10.807[J] .

L. Perez-Breva, D. Hart

2.912[J] Venture Engineering

Same subject as 3.085[J] , 15.373[J] Prereq: None U (Spring) 3-0-9 units

Provides an integrated approach to the development and growth of new innovative ventures. Intended for students who seek to leverage their engineering and science background through innovation-driven entrepreneurship. Emphasizes the concept that innovation-driven entrepreneurs must make a set of interdependent choices under conditions of high uncertainty, and demonstrates that venture engineering involves reducing uncertainty through a structured process of experimental learning and staged commitments. Provides deep understanding of the core technical, customer, and strategic choices and challenges facing start-up innovators, and a synthetic framework for the development and implementation of ventures in dynamic environments.

S. Stern, E. Fitzgerald

2.916[J] Money for Startups

Same subject as 10.407[J] Prereq: None G (Spring; second half of term) 2-0-4 units

See description under subject 10.407[J] .

S. Loessberg, D. P. Hart

2.96 Management in Engineering

Engineering School-Wide Elective Subject. Offered under: 2.96 , 6.9360 , 10.806 , 16.653 Prereq: None U (Fall) 3-1-8 units

Introduction and overview of engineering management. Financial principles, management of innovation, technical strategy and best management practices. Case study method of instruction emphasizes participation in class discussion. Focus is on the development of individual skills and management tools. Restricted to juniors and seniors.

H. S. Marcus, J.-H. Chun

2.961 Management in Engineering

Prereq: None G (Fall) 3-1-8 units

Introduction and overview of engineering management. Financial principles, management of innovation, technical strategy and best management practices. Case study method of instruction emphasizes participation in class discussion. Focus is on the development of individual skills and management tools.

J.-H. Chun, H. S. Marcus

2.965[J] Global Supply Chain Management

Same subject as 1.265[J] , 15.765[J] , SCM.265[J] Prereq: 15.761 , 15.778 , SCM.260[J] , SCM.261[J] , or permission of instructor G (Spring) Not offered regularly; consult department 2-0-4 units

See description under subject SCM.265[J] .

Advanced Topics and Special Subjects

2.98 sports technology: engineering & innovation.

Subject meets with 2.980 Prereq: None G (Spring) 2-2-2 units

Examines the future of sports technology across technical disciplines, including mechanical design, biomechanics, quantified self, sports analytics, and business strategies. Includes visits by leaders in the field to discuss various industries, career pathways, and opportunities for innovation in the field. Projects explore and potentially kickoff larger research and/or entrepreneurial initiatives.

A. Hosoi, C. Chase

2.980 Sports Technology: Engineering & Innovation

Subject meets with 2.98 Prereq: None U (Spring) 2-2-8 units

2.981 New England Coastal Ecology

Prereq: None U (IAP) 2-0-1 units

Provides exposure to marine communities found along the coast of New England and how they fit into global patterns. Focuses on the ecology of salt marshes and rocky shores, and the biology of plants and animals that live in these complex habitats. Prepares students to recognize common inhabitants of these two communities and develops understanding of the major environmental factors affecting them, the types of ecological services they provide, and likely impacts of current and future climate change. Includes visits to field and research centers. Limited to 20.

Consult C. Bastidas

2.982 Ecology and Sustainability of Coastal Ecosystems

Prereq: None U (Fall) Not offered regularly; consult department 3-2-4 units

Prepares students to recognize coastal ecosystems, their major environmental and biological drivers, and common impacts that human population growth and climate change have on them.  Students engage in a semester-long project to address and seek solutions to current challenges in sustainability of human activities on the coast, and to promote resilience of natural communities and ecosystem services.

J. Simpson, C. Bastidas

2.984[J] The Art and Science of Time Travel (New)

Same subject as CMS.343[J] Prereq: 8.02 and 18.02 G (Fall) 3-0-9 units

Explores time travel and other physical paradoxes—black holes, wormholes, and the multiverse—in the contexts of human narrative and contemporary scientific understanding. Instruction provided in the fundamental science of time travel in relativity and quantum mechanics. Students read and view classic time travel narratives in visual art and in film, and construct their own original time travel narratives. Limited to 20.

S. Lloyd, M. Reilly

2.989 Experiential Learning in Mechanical Engineering

Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Units arranged

Provides students the opportunity to learn and gain professional experience by participating in industrial projects related to Mechanical Engineering. Minimum project length is 10 weeks. Requires a written report upon completion. Before enrolling, students must contact MechE Graduate Office for procedures and restrictions; they must also have a firm internship offer and an identified MechE faculty member who will act as supervisor. Limited to Mechanical Engineering graduate students.

N. Hadjiconstantinou

2.990 Practical Experience

Prereq: None U (Fall, IAP, Spring, Summer) 0-1-0 units Can be repeated for credit.

For Mechanical Engineering undergraduates participating in curriculum-related off-campus experiences in mechanical engineering. Before enrolling, students must have an employment offer from a company or organization and must find a Mech E supervisor. Upon completion of the coursework the student must submit a detailed design notebook, approved by the MIT supervisor. Subject to departmental approval. Consult Department Undergraduate Office for details on procedures and restrictions.

Consult R. Karnik

2.991 Introduction to Graduate Study in Mechanical Engineering

Prereq: None G (Fall) 1-2-0 units

Familiarizes students with the requirements for their desired degree and the resources, both at MIT and beyond, to help them reach their educational and professional goals. Series of interactive lectures and seminars guides students through various aspects of life critical to navigating graduate school successfully. Topics include course requirements, PhD qualifying examinations, advisor/advisee relationships, funding and fellowships, mental health and wellbeing, housing options in the Boston area, and career options after graduation. Limited to first-year graduate students.

2.992 Professional Industry Immersion Project

Prereq: Permission of instructor G (Summer) Units arranged

Provides students a unique opportunity to participate in industry-based projects. Students gain professional industry experience in mechanical engineering projects that complement their academic experiences. Each project has a company supervisor, a specific advisor, and a course instructor. Course staff help students connect with specific companies and collaboratively design a project of mutual interest and benefit. Requires a written report and project presentation upon completion of a minimum of 10 weeks of off-campus activities. Limited to Mechanical Engineering graduate students.

2.993 Independent Study

Prereq: None U (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Designed for undergraduates wanting to continue substantial projects of own choice, under faculty supervision, in mechanical engineering. Work may be of experimental, theoretical, or design nature. Projects may be arranged individually in most fields of department interest, i.e., in mechanics, design and manufacturing, controls and robotics, thermal science and energy engineering, bioengineering, ocean engineering and nanotechnology. 2.993 is letter-graded; 2.994 is P/D/F.

2.994 Independent Study

Prereq: None U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

2.995 Advanced Topics in Mechanical Engineering

Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Assigned reading and problems or research in distinct areas, either theoretical or experimental, or design. Arranged on individual basis with instructor in the following areas: mechanics and materials, thermal and fluid sciences, systems and design, biomedical engineering, and ocean engineering. Can be repeated for credit only for completely different subject matter.

Consult R. Abeyaratne

2.996 Advanced Topics in Mechanical Engineering

2.997 advanced topics in mechanical engineering.

Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Not offered regularly; consult department Units arranged Can be repeated for credit.

2.998 Advanced Topics in Mechanical Engineering

2.s007 special subject in mechanical engineering.

Prereq: None U (Spring) Units arranged

Lecture, seminar or laboratory course consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter.

2.S009 Special Subject in Mechanical Engineering

Prereq: None U (Fall) Not offered regularly; consult department Units arranged

2.S19 Special Subject in Mechanical Engineering

B. Aulet, A. Hosoi, M. Jester, S. Johnson, C. Lawson

2.S372 Special Subject in Mechanical Engineering

Prereq: None G (Spring) Units arranged

Lecture, seminar, or laboratory consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter.

2.S670 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

2.S679 Undergraduate Special Subject in Mechanical Engineering

2.s790-2.s792 graduate special subject in bioengineering.

Advanced lecture, seminar or laboratory course consisting of material in the broadly-defined field of bioengineering not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter.

Consult R. Kamm

2.S793 Graduate Special Subject in Mechanical Engineering

Prereq: None G (Fall) Not offered regularly; consult department 3-3-6 units

Advanced lecture, seminar, or laboratory consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter.

2.S794 Graduate Special Subject in Mechanical Engineering

Prereq: None G (Fall) Units arranged [P/D/F]

2.S795 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Fall) Units arranged Can be repeated for credit.

2.S796 Special Subject in Mechanical Engineering

Prereq: None G (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit.

2.S885 Special Subject in Mechanical Engineering

Prereq: None U (Fall) Not offered regularly; consult department 3-3-6 units

2.S97 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Lecture, seminar or laboratory course consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 2.S972 - 2.S974 are graded P/D/F.

2.S971 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Fall) Not offered regularly; consult department 3-3-6 units Can be repeated for credit.

2.S972 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Fall, Spring) Not offered regularly; consult department 3-1-2 units Can be repeated for credit.

Consult K. Zolot

2.S973 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Fall) Units arranged [P/D/F] Can be repeated for credit.

2.S974 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit.

2.S975 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (IAP) Units arranged [P/D/F] Can be repeated for credit.

Lecture, seminar or laboratory course consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. See staff for scheduling information. Limited to 16.

Consult T. Consi

2.S976 Special Subject in Mechanical Engineering

2.s977 special subject in mechanical engineering, 2.s979 graduate special subject in mechanical engineering.

Prereq: None G (Fall) Not offered regularly; consult department Units arranged

2.S980 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Fall) Units arranged [P/D/F] Can be repeated for credit.

Advanced lecture, seminar, or laboratory consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 2.S980 and 2.S996 are graded P/D/F.

2.S981 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Spring) Units arranged Can be repeated for credit.

2.S982 Graduate Special Subject in Mechanical Engineering

Advanced lecture, seminar or laboratory consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 2.S980 and 2.S996 are graded P/D/F.

Consult V. Sudhir

2.S983 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit.

2.S984 Graduate Special Subject in Mechanical Engineering

Prereq: None G (Fall) Not offered regularly; consult department 3-0-9 units

2.S985 Special Subject in Mechanical Engineering

2.s986 special subject in mechanical engineering.

Prereq: None Acad Year 2023-2024: Not offered Acad Year 2024-2025: G (Spring) Units arranged

2.S987 Special Subject in Mechanical Engineering

Prereq: None G (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

S. Boriskina

2.S988 Special Subject in Mechanical Engineering

G. Traverso

2.S989 Undergraduate Special Subject in Mechanical Engineering

D. Frey, A. Talebinejad

2.S990 Graduate Special Subject in Mechanical Engineering

Prereq: None G (Spring) Units arranged Can be repeated for credit.

Lecture, seminar or laboratory course consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. Enrollment limited.

2.S991 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Spring) Not offered regularly; consult department Units arranged

Consult Staff

2.S992 Graduate Special Subject in Mechanical Engineering

A. Gopinath

2.S993 Undergraduate Special Subject in Mechanical Engineering

Prereq: None Acad Year 2023-2024: Not offered Acad Year 2024-2025: U (Spring) Units arranged Can be repeated for credit.

Lecture, seminar or laboratory course consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 2.S972 - 2.S974 , 2.S992 are graded P/D/F.

2.S994 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Spring) Units arranged Can be repeated for credit.

Lecture, seminar, or laboratory consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 2.S972 - 2.S974 and 2.S992 are graded P/D/F.

2.S995 Undergraduate Special Subject in Mechanical Engineering

Prereq: None U (Fall) 0-6-0 units Can be repeated for credit.

Consult I. Hunter

2.S996 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Fall, Spring) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit.

2.S997 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Consult F. Ahmed

2.S998 Graduate Special Subject in Mechanical Engineering

Consult R. Abeyaratne, J. Hart

2.S999 Graduate Special Subject in Mechanical Engineering

Prereq: Permission of instructor G (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

Consult R. Abeyaratne, T. Gutowski

Thesis, Research and Practice

2.978 instruction in teaching engineering.

Subject meets with 1.95[J] , 5.95[J] , 7.59[J] , 8.395[J] , 18.094[J] Prereq: Permission of instructor G (Fall) Units arranged [P/D/F]

Participatory seminar focuses on the knowledge and skills necessary for teaching engineering in higher education. Topics include research on learning; course development; promoting active learning, problemsolving, and critical thinking in students; communicating with a diverse student body; using educational technology to further learning; lecturing; creating effective tests and assignments; and assessment and evaluation. Field-work teaching various subjects in the Mechanical Engineering department will complement classroom discussions.

2.979 Undergraduate Teaching

Prereq: None U (Fall, IAP, Spring) Units arranged [P/D/F] Can be repeated for credit.

For students participating in departmentally approved undergraduate teaching programs. Students assist faculty in the design and execution of the curriculum and actively participate in the instruction and monitoring of the class participants. Students prepare subject materials, lead discussion groups, and review progress. Credit is arranged on a subject-by-subject basis and is reviewed by the department.

A. E. Hosoi

2.999 Engineer's Degree Thesis Proposal Preparation

Prereq: Permission of instructor G (Fall, Spring, Summer) Units arranged Can be repeated for credit.

For students who must do additional work to convert an SM thesis to a Mechanical Engineer's (ME) or Naval Engineer's (NE) thesis, or for students who write an ME/NE thesis after having received an SM degree.

R. Abeyaratne, M. S. Triantafyllou

2.C01 Physical Systems Modeling and Design Using Machine Learning

Subject meets with 2.C51 Prereq: 2.086 ; Coreq: 6.C01 U (Spring; second half of term) 1-3-2 units Credit cannot also be received for 1.C01 , 1.C51 , 2.C51 , 3.C01[J] , 3.C51[J] , 10.C01[J] , 10.C51[J] , 20.C01[J] , 20.C51[J] , 22.C01 , 22.C51 , SCM.C51

Building on core material in 6.C01 , encourages open-ended exploration of the increasingly topical intersection between artificial intelligence and the physical sciences. Uses energy and information, and their respective optimality conditions, to define supervised and unsupervised learning algorithms as well as ordinary and partial differential equations. Subsequently, physical systems with complex constitutive relationships are drawn from elasticity, biophysics, fluid mechanics, hydrodynamics, acoustics, and electromagnetics to illustrate how machine learning-inspired optimization can approximate solutions to forward and inverse problems in these domains. Students taking graduate version complete additional assignments. Students cannot receive credit without simultaneous completion of 6.C01 .

2.C27[J] Computational Imaging: Physics and Algorithms (New)

Same subject as 3.C27[J] , 6.C27[J] Subject meets with 2.C67[J] , 3.C67[J] , 6.C67[J] Prereq: 18.C06[J] and ( 1.00 , 1.000 , 2.086 , 3.019 , or 6.100A ) U (Fall) 3-0-9 units

Explores the contemporary computational understanding of imaging: encoding information about a physical object onto a form of radiation, transferring the radiation through an imaging system, converting it to a digital signal, and computationally decoding and presenting the information to the user. Introduces a unified formulation of computational imaging systems as a three-round "learning spiral": the first two rounds describe the physical and algorithmic parts in two exemplary imaging systems. The third round involves a class project on an imaging system chosen by students. Undergraduate and graduate versions share lectures but have different recitations. Involves optional "clinics" to even out background knowledge of linear algebra, optimization, and computational imaging-related programming best practices for students of diverse disciplinary backgrounds. Students taking graduate version complete additional assignments.

G. Barbastathis, J. LeBeau, R. Ram, S. You

2.C51 Physical Systems Modeling and Design Using Machine Learning

Subject meets with 2.C01 Prereq: 18.0751 or 18.0851 ; Coreq: 6.C51 G (Spring; second half of term) 1-3-2 units Credit cannot also be received for 1.C01 , 1.C51 , 2.C01 , 3.C01[J] , 3.C51[J] , 10.C01[J] , 10.C51[J] , 20.C01[J] , 20.C51[J] , 22.C01 , 22.C51 , SCM.C51

Building on core material in 6.C51 , encourages open-ended exploration of the increasingly topical intersection between artificial intelligence and the physical sciences. Uses energy and information, and their respective optimality conditions, to define supervised and unsupervised learning algorithms as well as ordinary and partial differential equations. Subsequently, physical systems with complex constitutive relationships are drawn from elasticity, biophysics, fluid mechanics, hydrodynamics, acoustics, and electromagnetics to illustrate how machine learning-inspired optimization can approximate solutions to forward and inverse problems in these domains. Students taking graduate version complete additional assignments. Students cannot receive credit without simultaneous completion of 6.C51 .

2.C67[J] Computational Imaging: Physics and Algorithms (New)

Same subject as 3.C67[J] , 6.C67[J] Subject meets with 2.C27[J] , 3.C27[J] , 6.C27[J] Prereq: 18.C06[J] and ( 1.00 , 1.000 , 2.086 , 3.019 , or 6.100A ) G (Fall) 3-0-9 units

Contemporary understanding of imaging is computational: encoding onto a form of radiation the information about a physical object, transferring the radiation through the imaging system, converting it to a digital signal, and computationally decoding and presenting the information to the user. This class introduces a unified formulation of computational imaging systems as a three-round "learning spiral": the first two rounds, instructors describe the physical and algorithmic parts in two exemplary imaging systems. The third round, students conduct themselves as the class project on an imaging system of their choice. The undergraduate and graduate versions share lectures but have different recitations. Throughout the term, we also conduct optional "clinics" to even out background knowledge of linear algebra, optimization, and computational imaging-related programming best practices for students of diverse disciplinary backgrounds.

2.EPE UPOP Engineering Practice Experience

Engineering School-Wide Elective Subject. Offered under: 1.EPE , 2.EPE , 3.EPE , 6.EPE , 8.EPE , 10.EPE , 15.EPE , 16.EPE , 20.EPE , 22.EPE Prereq: None U (Fall, Spring) 0-0-1 units Can be repeated for credit.

Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.

K. Tan-Tiongco, D. Fordell

2.EPW UPOP Engineering Practice Workshop

Engineering School-Wide Elective Subject. Offered under: 1.EPW , 2.EPW , 3.EPW , 6.EPW , 10.EPW , 16.EPW , 20.EPW , 22.EPW Prereq: 2.EPE U (IAP, Spring) 1-0-0 units

Provides sophomores across all majors with opportunities to develop and practice communication, teamwork, and problem-solving skills to become successful professionals in the workplace, particularly in preparation for their summer industry internship. This immersive, multi-day Team Training Workshop (TTW) is comprised of experiential learning modules focused on expanding skills in areas that employers report being most valuable in the workplace. Modules are led by MIT faculty with the help of MIT alumni and other senior industry professionals. Skills applied through creative simulations, team problem-solving challenges, oral presentations, and networking sessions with prospective employers. Enrollment limited to those in the UPOP program.

2.THG Graduate Thesis

Prereq: Permission of advisor G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Program of research leading to the writing of an SM, PhD, or ScD thesis; to be arranged by the student and an appropriate MIT faculty member.

2.THU Undergraduate Thesis

Individual self-motivated study, research, or design project under faculty supervision. Departmental program requirement: minimum of 6 units. Instruction and practice in written communication provided.

2.UR Undergraduate Research in Mechanical Engineering

Individual study, research, or laboratory investigations under faculty supervision, including individual participation in an ongoing research project. See projects listing in Undergraduate Office, 1-110, for guidance.

Consult D. Rowell

2.URG Undergraduate Research in Mechanical Engineering

Consult N. Fang, K. Kamrin

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FUTURES IN MECHANICAL ENGINEERING

Explore graduate school with mit’s department of mechanical engineering.

Launched in 2020 by MIT’s Department of Mechanical Engineering, the Futures in Mechanical Engineering program encourages and supports individuals interested in pursuing a graduate degree in mechanical engineering; particularly those who have historically been underrepresented in our field. 

Each year we share information about our graduate program and advice on how to apply via virtual event(s) and timely emails. Prospective undergraduate students in mechanical engineering are invited to utilize the resources on this site and join our email list to receive a small number of emails in advance of our Graduate Application Deadline which is December 15, 2023.

While we will share information about MIT’s mechanical engineering graduate program in particular, our goal is to encourage more women and individuals from underrepresented backgrounds to pursue advanced degrees in mechanical engineering across the board.

Connect with MIT Mechanical Engineering

The MIT Mechanical Engineering Graduate Office provides comprehensive support for prospective students.  The MechE Graduate Webpage and the “ Applying for Admissions ” page are key resources for prospective students.

Our Graduate Office Team Dan Shea, Una Sheehan, Saana McDaniel (Graduate Academic Administrator), and Laura Zaganjori (not pictured) are always happy to answer any questions as you prepare to apply to our program.

Contact the Grad Office team at [email protected]

MIT’s Virtual Graduate Fair: November 15, 2023

MIT Virtual Graduate Fair

Wednesday, november 15, 2023, noon-2:00pm edt.

MIT’s Department of Mechanical Engineering is one of many departments participating in the first annual “MIT Virtual Graduate Fair” sponsored by the Office of Graduate Education . Tap into the Mind + Heart of MIT and join us for a virtual showcase of MIT’s graduate programs, summer research and post doctoral opportunities!

On-Demand Video Resources

Video on-demand: overview of graduate school at mit's department of mechanical engineering.

Not sure if graduate school in mechanical engineering (or MIT specifically) is right for you? In this video,  Dr. Dawn Wendell shares about the structure and supports of the MIT Mechanical Engineering graduate program and reflections on why one might choose to pursue graduate school.

Video On-Demand: Strategies for Grad School and Fellowship Applications

Are you seeking advice on how to develop the content and structure of your application to graduate school or graduate fellowships? In this video, Dr. Svetlana Boriskina, Principal Research Scientist and Manager of the MechE Communications Lab shares insights from her vast experience advising students in this area.

• Core Members
• Affiliate Members
• Interdisciplinary Doctoral Program in Statistics
• Minor in Statistics and Data Science
• MicroMasters program in Statistics and Data Science
• Data Science and Machine Learning: Making Data-Driven Decisions
• Norbert Wiener Fellowship
• Stochastics and Statistics Seminar
• IDSS Distinguished Seminars
• IDSS Special Seminar
• SDSC Special Events
• Online events
• IDS.190 Topics in Bayesian Modeling and Computation
• Past Events
• LIDS & Stats Tea
• Interdisciplinary PhD in Mechanical Engineering and Statistics

Requirements: Students must complete their primary program’s degree requirements along with the IDPS requirements. Statistics requirements must not unreasonably impact performance or progress in a student’s primary degree program.

Grade Requirements:  B+ in all required coursework (see options below) PhD Earned on Completion: Mechanical Engineering and Statistics

IDPS/Mechanical Engineering Chair : Themistoklis Sapsis

MIT Statistics + Data Science Center Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139-4307 617-253-1764

• Accessibility
• Interdisciplinary PhD in Aero/Astro and Statistics
• Interdisciplinary PhD in Brain and Cognitive Sciences and Statistics
• Interdisciplinary PhD in Economics and Statistics
• Interdisciplinary PhD in Mathematics and Statistics
• Interdisciplinary PhD in Physics and Statistics
• Interdisciplinary PhD in Political Science and Statistics
• Interdisciplinary PhD in Social & Engineering Systems and Statistics
• LIDS & Stats Tea
• Spring 2023
• Spring 2022
• Spring 2021
• Fall – Spring 2020
• Fall 2019 – IDS.190 – Topics in Bayesian Modeling and Computation
• Fall 2019 – Spring 2019
• Fall 2018 and earlier

Statement of Purpose for Graduate School

Criteria for success.

•   qualified for their program, and
• a good fit for their program’s focus and goals.
• You show a select group of skills and experiences that concisely convey your scientific accomplishments and interests.
• Your experiences are concrete and quantitative .
• Your personal statement is no more than 2 pages (less if you can, or if it is required by the school).

Structure Diagram

The graduate school Personal Statement (≈ Statement of Purpose ≈ Statement of Intent) is a document that complements your resume and application form, describing your profile in a narrative way and convincing the admission committee that you would be a good match for a particular department or program. Take into account that matching goes both ways: they should be interested in you, and you should be interested in them. Your personal statement should make this match clear.

Analyze Your Audience

Your personal statement will be read by a graduate committee – a handful of faculty from the program. They’re trying to determine if you will be a successful graduate student in their department and a successful scientist after you graduate. They are interested in your qualifications as a researcher, your career goals, and how your personality matches their labs and department.

The graduate committee probably reads hundreds of applications every year. To make it easy for them to figure out that you are a good fit, keep in mind the following suggestions:

• Make direct, concrete statements about your accomplishments and qualifications.
• Create a narrative that serves as a personal brand and helps them remember you.
• Give them some unique examples that describe you and make you stand out, and which will make them remember you as “that candidate that was so passionate about…” or “who has a lot of experience in…”, although they might not remember your name.
• Align your academic goals and motivations with specific research projects or research directions of the target department. 

Assessing your match to the target program

A key point on writing your Personal Statement is to demonstrate that you have done previous research about the program to which you’re applying, that you understand its characteristics and objectives, and that you are really interested in joining it and willing to do your best to be successful in it. To do this:

• Read the program’s website. Learn about its faculty members and the projects they are working on. Check what topics and high level goals the department is committed to. Identify the main research areas. 
• Get in contact with faculty and students in your target program. Browse recent publications and presentations but remember lab websites can be outdated and a publication may lag a few years behind the active research in a lab so pay attention to the motivation, direction, and methods of the faculty member over specific results. If you have had a positive discussion with someone at the department, you can include in your essay how those interactions confirmed that you would be a good match for the program.

Reflect before you start

To convince a graduate committee that you are ready for and excited about graduate school, first you need to be able to articulate this to yourself. Earnestly reflect on the following types of questions. A lack of authenticity is easy to detect. 

• Why do I want to go to graduate school? 
• How am I sure?
• Why will I be successful in graduate school?
• What can I do with the help of this degree that I couldn’t do before?
• Where do I want to be in a few years?
• How am I going to get there?

Create a personal narrative

Graduate programs invest in the professional and scientific growth of their students. Get the committee excited about investing in you by opening your essay with a brief portrait of what drives you as a scientist. What research directions are you passionate about, and why? What do you picture yourself doing in 10 years?

• E.g. “Graduate study is the first step towards my goal: I want to improve my ability as a researcher and gain more technical depth and breadth to maximize my impact. In the long term, I hope graduate school will better position me to be a leader in shaping the conversation about what problems can be addressed by mechanical engineers.”

Close your essay with a 2-3 sentence discussion of your long-term career interests. No one will hold you to this; this just helps your committee visualize your potential trajectory.

• E.g. “Above all else, a MIT PhD would help me achieve my long term career goal of becoming a professor, the position in which I can best see myself accomplishing my mission to show others the hidden beauty in everyday life through science.”

Connect your personal narrative to whichever degree you are applying to (be it research-based or course-work-based, or a Master of Science, Master of Engineering, or PhD). Especially in mechanical engineering, each of these degrees will enable different career trajectories and provide different educational opportunities. Articulate clearly why the degree you are applying for helps you achieve your goals. In the same vein, consider mutual benefit: what will you contribute to the academic community over your time at your target school? Remember, it all comes back to “qualified match” , no matter what level of degree you are applying for. 

Describe your experiences

Experiences are the “what” of your essay. They are the most efficient and easiest way to prove your capabilities to the admissions committee.

• What experiences led you to develop your skill set and passions ?
• Where have you demonstrated accomplishment, leadership, and collaboration?
• Show your depth with a range of experiences: research, teaching, relevant extracurriculars and leadership positions.
• State concrete achievements and outcomes like awards, discoveries, or publications, or projects completed.

Achievements need not be limited to research projects or publications. Think about all the experiences that demonstrate your ability to conduct research and succeed within the structure of your target program. (Where have you demonstrated creativity? Self sufficiency? Perseverance? What open ended problems have you tackled? What enabled you to succeed at them?)

Quantify your experiences to show concrete impact. How many people were on your team? How many protocols did you develop? How many people were in competition for an award? As a TA, how often did you meet with your students?

For each experience you include, focus on how the experience affected you. Describe your actions, and always direct the message to highlighting your performance and growth (not how important the company was or how well-known the professor you TAed for is). Remember, it is not an essay about science, it is a personal essay—about you and how you have positioned yourself to succeed in graduate school.

Explain the meaning of your experiences

Your goal in sharing your experiences is to demonstrate that you have the qualifications, qualities, and drive needed to succeed in graduate school. Therefore, you will need to not only choose experiences wisely but also state specifically what they mean within the context of your application.

• Why was this experience important to your growth as a scientist?
• What did you gain from or demonstrate during that experience?
• How will this make you a better grad student?

Even if it feels obvious to you, you need to explicitly answer these questions to your audience. Here are some examples experiences that have been expanded to contain meaning:

Contemplate how disparate activities can be unified into a common narrative about your motivations and achievements. Articulate this clearly to make your statement cohesive.

Demonstrate your match to the target program

Using the research you did to assess your chosen programs, clearly articulate why you are a match . Consider both directions of the match: not only why you want to go to the school, but also why you would fit in well and contribute to the program.

State which professors in the program you would be interested in working with. Demonstrate that you have done your homework regarding the program. Show how their research areas align with your background and your goals. If you have had conversations with students or professors in the program, be sure to include that as well. 

Common Pitfalls

Write about you , not your role models. One of the most common pitfalls we see in the Comm Lab is students writing touching Personal Statements about family members or role models who have inspired them. There is nothing wrong with including personal stories about people who have helped you understand yourself better, or positioned you to succeed in graduate school, but it is important to tread very carefully. Don’t leave the reader wondering why they are reading about someone else in a document that is meant to be about you. If you take time to talk about someone who positively affected you, make sure to be very clear about how that experience with that person molded you into a strong graduate school candidate.

Be judicious with childhood stories. A brief mention of some childhood experience that shaped your interests in STEM is probably okay, but if you talk about it at length (more than ~2 sentences), you are taking up space that should probably be used to talk about who you are today, not who you were over a decade ago.

Don’t simply restate your resume. Your Personal Statement should be a technical document (having evidence, numbers, and supporting facts) with personal outcomes (talking about your motivations, ambitions, and ability to succeed as a graduate student). Of course, you will reiterate parts of your resume in your Personal Statement , but what uniquely makes it a “Personal Statement” is the discussion of how those professional experiences affected you , as a researcher and person well-suited to the graduate program at X University.  

Insufficient quantification of your experiences. We are all scientists and engineers; our line of work is inherently quantitative. Quantification is a quick and easy way to add context, lend credence to your experiences, and impress the reader. Even little quantifications can help: “I spent two semesters working on a project about…” is much better than “I spent some time working on a project about…”. See more examples in the section on Experiences, above.

Being a great student and having an impressive resume is only half the battle when it comes to graduate school applications. You need to be able to communicate and convince the committee that your personality and particular set of skills and experiences are well-suited to the graduate program you are applying for. This extends beyond graduate school applications: as scientists and engineers, we write papers and technical reports to communicate with our peers and convince them that our work is meaningful.

By reading this article, you have recognized the value of communication and are well on your way to crafting an effective and powerful Personal Statement. This is your opportunity to make yourself shine among all the other candidates, so make it count! You can do it!

Acknowledgements : This content was adapted from the NSE and CEE Communication Labs’ CommKits for graduate applications.

Resources and Annotated Examples

Annotated example 1, annotated example 2.

EDUCATION @ MIT MECHE

Pursue your vision in a meche graduate program.

Earning a graduate degree from MechE hones your engineering skills through project-based learning, arming you with the technical acumen, creative spirit, and real-world experience to make a difference in the areas that matter to you most.

Scroll to Explore

• Grad Student Resources
• Applying for Admission
• Financial Support
• Enrolling Once Admitted
• Professional Development

Explore Our Graduate Programs

• News + Media
• Student Groups

MIT Graduate Admissions Policy Update

The department of Mechanical Engineering will not require GRE tests for applications for graduate admission for 2024, nor will we use GRE scores as a basis for evaluating candidates for admission in the 2024 application process.

We offer 9 Graduate Degrees

Master of Science in Mechanical Engineering (SMME)

Master of Science in Ocean Engineering (SMOE)

Master of Science in Naval Architecture and Marine Engineering (SMNAME)

Master of Science in Oceanographic Engineering (SMOGE, joint MIT/WHOI degree)

Master of Engineering in Manufacturing

Mechanical Engineer’s (ME) Degree

Naval Engineer’s (NE) Degree

Doctor of Philosophy (PhD) or Doctor of Science (ScD), which differs in name only (this includes the joint MIT/WHOI degrees)

Dual degree with Leaders for Global Operations (LGO) Program in MIT Sloan School of Management (Please go to the following website: https://lgo.mit.edu/ to learn more about applying through LGO.)

Meet Some of Our Students

Healing with hydrogels

Engineering art

Saving Seaweed with Machine Learning

Graduate Resources

• Guide to Graduate Study
• Key Dates and Deadlines
• Fabrication shops
• Graduate Qualifying Exam Guide
• Communications Lab

Graduate Program News + Media

Engineering Medical Devices

Mechanical engineering students from MIT work with clinicians from Boston-area hospitals to design cheaper, safer, and more efficient medical devices.

Peer coaching helps graduate students thrive

The Graduate Student Coaching Program created by Kelli Hendrickson PhD '05 teaches students the “coaching mindset” to help them reach their personal and professional goals.

The breadth of MechE

Across MechE, faculty and staff are engaging in cutting-edge research at the frontiers of a new vision for mechanical engineering.

Meet Some of Our Faculty

• bioengineering

Join a Student Group, Or Two

Alumni spotlight.

Senior Scientist, Woods Hole Oceanographic Institution

Senior VP and General Manager, Qualcomm MEMS Technologies

Leigh Fibers

Graduate Office Contacts

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• Commencement 2023

Simultaneously lab and playground, MIT is unlike any other place on Earth.

Walking through the halls of the Institute feels like walking into the future: four-legged robots leaping over obstacles; researchers hunched over microscopes untangling the fundamental properties of graphene; makers building nanosatellites, or wearable electronics, or even a roller coaster.

Here, students hurry to class yammering about quantum computing, CRISPR gene editing, and nuclear fusion — sometimes in the same conversation.

MIT is nerd heaven, a place where that word implies nothing but muscle and credibility. We value merit, rigor, ingenuity, and real-world problem-solving. This is where bright minds come from every corner of the Earth to make something new — and make something of themselves.

In this community, we believe as much in excellence and boldness as we do in humility and the value of failure. An open spirit of collaboration. A strong desire to make a positive impact. And a sense of responsibility to make the world a better place.

We encourage you to visit campus, explore Cambridge and Boston, talk to current students and faculty, and get to know our community in person.

You will find, in the words of one of our students, that “the MIT culture is very accepting.” And we wouldn’t have it any other way.

Advanced Manufacturing and Design Innovation @ MIT

In just 12 months the MIT Master of Engineering in Manufacturing (MEng) prepares you to not only assume professional leadership positions, but also provides you with the necessary skill set and confidence to affect transformative and innovative change within manufacturing industries.

To apply to the MEng program, you must apply to the  Mechanical Engineering Graduate program  and specify “Master of Engineering in Advanced Manufacturing and Design” on the application. Also, in addition to your statement of objectives, supplemental essays must be completed for your application to be considered. You must also submit a Mechanical Engineering application. Please visit the  MIT Department of Mechanical Engineering Graduate Office  to access the online application. Please visit our  Application Materials page  to review the list of required application materials. 

Applications will be accepted until December 15th.

Approximate Application-Process Timeline

• October through December 15th:  Applications are submitted by prospective students
• The Mechanical Engineering Graduate Office receives all submitted graduate applications and supplemental materials
• December 15th through early March:  Completed applications are circulated to and evaluated by the MEngM application committee members
• Mid-March through April 1:  Admission decisions are made by committee members
• Applicants are notified by email by the Mechanical Engineering Graduate Office of their admission status.
• April 15:  Deadline for applicants to accept or decline admission offer to MIT
• Applications Materials
• Testing Requirements
• Financial Information
• MicroMasters
• Industry Projects
• Manufacturing Careers
• Accessibility

100 Best universities for Mechanical Engineering in Russia

Updated: February 29, 2024

• Art & Design
• Computer Science
• Engineering
• Environmental Science
• Liberal Arts & Social Sciences
• Mathematics

Below is a list of best universities in Russia ranked based on their research performance in Mechanical Engineering. A graph of 714K citations received by 136K academic papers made by 158 universities in Russia was used to calculate publications' ratings, which then were adjusted for release dates and added to final scores.

We don't distinguish between undergraduate and graduate programs nor do we adjust for current majors offered. You can find information about granted degrees on a university page but always double-check with the university website.

1. Moscow State University

For Mechanical Engineering

2. Tomsk State University

3. St. Petersburg State University

4. Bauman Moscow State Technical University

5. Ufa State Aviation Technical University

6. Peter the Great St.Petersburg Polytechnic University

7. Tomsk Polytechnic University

8. Ural Federal University

9. South Ural State University

10. National Research University Higher School of Economics

11. Moscow Aviation Institute

12. Novosibirsk State University

13. ITMO University

14. N.R.U. Moscow Power Engineering Institute

15. National Research Nuclear University MEPI

16. Kazan Federal University

17. National University of Science and Technology "MISIS"

18. Moscow Institute of Physics and Technology

19. Samara National Research University

20. Moscow State Technological University "Stankin"

21. Novosibirsk State Technical University

22. RUDN University

23. Southern Federal University

24. Saratov State University

25. Ufa State Petroleum Technological University

26. Samara State Technical University

27. Siberian Federal University

28. Kazan National Research Technical University named after A.N. Tupolev - KAI

29. Perm State Technical University

30. Omsk State Technical University

31. Saint Petersburg State Electrotechnical University

32. Moscow Polytech

33. Saint-Petersburg Mining University

34. Magnitogorsk State Technical University

35. Saratov State Technical University

36. Moscow State University of Railway Engineering

37. Lobachevsky State University of Nizhni Novgorod

38. Nizhny Novgorod State Technical University

39. Tula State University

40. Belgorod State Technological University

41. Far Eastern Federal University

42. Novgorod State University

43. belgorod state university.

44. Finance Academy under the Government of the Russian Federation

45. Moscow Medical Academy

46. Kazan State Technological University

47. Russian State University of Oil and Gas

48. siberian state aerospace university.

49. Tambov State Technical University

50. Voronezh State University

51. Siberian State Industrial University

52. Saint Petersburg State Institute of Technology

53. Kalashnikov Izhevsk State Technical University

54. St. Petersburg State University of Architecture and Civil Engineering

55. Mendeleev University of Chemical Technology of Russia

56. Murmansk State Technical University

57. South-Western State University

58. Ogarev Mordovia State University

59. Tomsk State University of Control Systems and Radioelectronics

60. south-russian state university of economics and service.

61. Perm State University

62. Kuzbass State Technical University

63. Russian National Research Medical University

64. Plekhanov Russian University of Economics

65. Ulyanovsk State Technical University

66. Ulyanovsk State University

67. Penza State University

68. Kuban State University of Technology

69. Polzunov Altai State Technical University

70. Chelyabinsk State University

71. Yaroslavl State University

72. University of Tyumen

73. National Research University of Electronic Technology

74. Leningrad State University

75. Moscow State Pedagogical University

76. Udmurt State University

77. Irkutsk State University

78. North-Eastern Federal University

79. Bashkir State University

80. Russian Presidential Academy of National Economy and Public Administration

81. Kuban State University

82. Kuban State Agricultural University

83. St. Petersburg State University of Aerospace Instrumentation

84. Kemerovo State University

85. Immanuel Kant Baltic Federal University

86. Orenburg State University

87. Baltic State Technical University "Voenmeh"

88. Tomsk State University of Architecture and Building

89. Chuvash State University

90. ivanovo state power university.

91. Irkutsk National Research Technical University

92. Orel State University

93. State University of Management

94. Tomsk State Pedagogical University

95. Volgograd State University

96. Petrozavodsk State University

97. Tver State University

98. Northern Arctic Federal University

99. Omsk State Transport University

100. Kaliningrad State Technical University

The best cities to study Mechanical Engineering in Russia based on the number of universities and their ranks are Moscow , Tomsk , Saint Petersburg , and Ufa .

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Twenty-three MIT faculty, five from Physics, honored as “Committed to Caring” for 2023-25

The honor recognizes professors for their outstanding mentorship of graduate students..

In the halls of MIT, a distinctive thread of compassion weaves through the fabric of education. As students adjust to a postpandemic normal, many professors have played a pivotal role by helping them navigate the realities of hybrid learning and a rapidly changing postgraduation landscape. 

The Committed to Caring (C2C) program at MIT is a student-driven initiative that celebrates faculty members who have served as exceptional mentors to graduate students. Twenty-three MIT professors have been selected as recipients of the C2C award for 2023-25, marking the most extensive cohort of honorees to date. These individuals join the ranks of 75 previous C2C honorees. 

The actions of these MIT faculty members over the past two years underscore their profound commitment to the well-being, growth, and success of their students. These educators go above and beyond their roles, demonstrating an unwavering dedication to mentorship, inclusion, and a holistic approach to student development. They aim to create a nurturing environment where students not only thrive academically, but also flourish personally. 

The following faculty members are the 2023-25 Committed to Caring honorees:

• Hamsa Balakrishnan, Department of Aeronautics and Astronautics
• Cynthia Breazeal, Media Lab
• Roberto Fernandez, MIT Sloan School of Management
• Nuh Gedik , Department of Physics
• Mariya Grinberg, Department of Political Science
• Ming Guo, Department of Mechanical Engineering
• Myriam Heiman, Department of Brain and Cognitive Sciences
• Rohit Karnik, Department of Mechanical Engineering
• Erik Lin-Greenberg, Department of Political Science
• Michael McDonald , Department of Physics
• Emery Neal Brown, Harvard-MIT Program in Health Sciences and Technology
• Wanda Orlikowski, MIT Sloan School of Management
• Kenneth Oye, Department of Political Science
• Kristala Prather, Department of Chemical Engineering
• Zachary Seth Hartwig, Department of Nuclear Science and Engineering
• Tracy Slatyer , Department of Physics
• Iain Stewart , Department of Physics
• Andrew Vanderburg , Department of Physics
• Rodrigo Verdi, MIT Sloan School of Management
• Xiao Wang, Department of Chemistry
• Ariel White, Department of Political Science
• Nathan Wilmers, MIT Sloan School of Management
• Maria Yang, Department of Mechanical Engineering

Since the founding of the C2C program in 2014 by the Office of Graduate Education, the nomination process for honorees has centered on student involvement. Graduate students from all departments are invited to submit nomination letters detailing professors’ outstanding mentorship practices. A committee of graduate students and staff members then selects individuals who have shown genuine contributions to MIT’s vibrant academic community through student mentorship.

The selection committee this year included: Maria Carreira (Biology), Rima Das (Mechanical Engineering), Ahmet Gulek (Economics), Bishal Thapa (Biological Engineering), Katie Rotman (Architecture), Dóra Takács (Linguistics), Dan Korsun (Nuclear Science and Engineering), Leslie Langston (Student Mental Health and Counseling), Patricia Nesti (MIT-Woods Hole Oceanographic Institution), Beth Marois (Office of Graduate Education [OGE]), Sara Lazo (OGE), and Chair Suraiya Baluch (OGE).  

This year’s nomination letters highlighted unique stories of how students felt supported by professors. Students noted their mentors’ commitment to frequent meetings despite their own busy personal lives, as well as their dedication to ensuring equal access to opportunities for underrepresented and underserved students.

Some wrote about their advisors’ careful consideration of students’ needs alongside their own when faced with professional advancement opportunities; others appreciated their active support for students in the LGBTQ+ community. Lastly, students reflected on their advisors’ encouragement for open and constructive discourse around the graduate unionization vote, showing a genuine desire to hear about graduate issues.

Baluch shared, “Working with the amazing selection committee was the highlight of my work year. I was so impressed by the thoughtful consideration each nomination received. Selecting the next round of C2C nominees is always a heartwarming experience.” 

“As someone who aspires to be a faculty member someday,” noted Das, “being on the selection committee … was a phenomenal opportunity in understanding the breadth and depth of possibility in how to be a caring mentor in academia.”

She continued, “It was so heartening to hear the different ways that these faculty members are going above and beyond their explicit research and teaching duties and the amazing impact that has made on so many students’ well-being and ability to be successful in graduate school.” 

The Committed to Caring program continues to reinforce MIT’s culture of mentorship, inclusion, and collaboration by recognizing the contributions of outstanding professors. In the coming months, news articles will feature pairs of honorees, and a reception will be held in May.

Related News

Four MIT faculty named 2023 AAAS Fellows

Erin Kara named Edgerton Award winner

Tracy Slatyer awarded 2024 Guggenheim Fellowship

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Best Global Universities for Mechanical Engineering in Russia

These are the top universities in Russia for mechanical engineering, based on their reputation and research in the field. Read the methodology »

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Here are the best global universities for mechanical engineering in Russia

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• Twenty-three MIT faculty honored as "Committed to Caring" for 2023-25

Twenty-three MIT faculty honored as "Committed to Caring" for 2023-25

Press contact :.

Previous image Next image

In the halls of MIT, a distinctive thread of compassion weaves through the fabric of education. As students adjust to a postpandemic normal, many professors have played a pivotal role by helping them navigate the realities of hybrid learning and a rapidly changing postgraduation landscape. 

The Committed to Caring (C2C) program at MIT is a student-driven initiative that celebrates faculty members who have served as exceptional mentors to graduate students. Twenty-three MIT professors have been selected as recipients of the C2C award for 2023-25, marking the most extensive cohort of honorees to date. These individuals join the ranks of 75 previous C2C honorees. 

The actions of these MIT faculty members over the past two years underscore their profound commitment to the well-being, growth, and success of their students. These educators go above and beyond their roles, demonstrating an unwavering dedication to mentorship, inclusion, and a holistic approach to student development. They aim to create a nurturing environment where students not only thrive academically, but also flourish personally. 

The following faculty members are the 2023-25 Committed to Caring honorees:

• Hamsa Balakrishnan, Department of Aeronautics and Astronautics
• Cynthia Breazeal, Media Lab
• Roberto Fernandez, MIT Sloan School of Management
• Nuh Gedik, Department of Physics
• Mariya Grinberg, Department of Political Science
• Ming Guo, Department of Mechanical Engineering
• Myriam Heiman, Department of Brain and Cognitive Sciences
• Rohit Karnik, Department of Mechanical Engineering
• Erik Lin-Greenberg, Department of Political Science
• Michael McDonald, Department of Physics
• Emery Neal Brown, Harvard-MIT Program in Health Sciences and Technology
• Wanda Orlikowski, MIT Sloan School of Management
• Kenneth Oye, Department of Political Science
• Kristala Prather, Department of Chemical Engineering
• Zachary Seth Hartwig, Department of Nuclear Science and Engineering
• Tracy Slatyer, Department of Physics
• Iain Stewart, Department of Physics
• Andrew Vanderburg, Department of Physics
• Rodrigo Verdi, MIT Sloan School of Management
• Xiao Wang, Department of Chemistry
• Ariel White, Department of Political Science
• Nathan Wilmers, MIT Sloan School of Management
• Maria Yang, Department of Mechanical Engineering

Since the founding of the C2C program in 2014 by the Office of Graduate Education, the nomination process for honorees has centered on student involvement. Graduate students from all departments are invited to submit nomination letters detailing professors’ outstanding mentorship practices. A committee of graduate students and staff members then selects individuals who have shown genuine contributions to MIT’s vibrant academic community through student mentorship.

The selection committee this year included: Maria Carreira (Biology), Rima Das (Mechanical Engineering), Ahmet Gulek (Economics), Bishal Thapa (Biological Engineering), Katie Rotman (Architecture), Dóra Takács (Linguistics), Dan Korsun (Nuclear Science and Engineering), Leslie Langston (Student Mental Health and Counseling), Patricia Nesti (MIT-Woods Hole Oceanographic Institution), Beth Marois (Office of Graduate Education [OGE]), Sara Lazo (OGE), and Chair Suraiya Baluch (OGE).  

This year’s nomination letters highlighted unique stories of how students felt supported by professors. Students noted their mentors’ commitment to frequent meetings despite their own busy personal lives, as well as their dedication to ensuring equal access to opportunities for underrepresented and underserved students.

Some wrote about their advisors’ careful consideration of students’ needs alongside their own when faced with professional advancement opportunities; others appreciated their active support for students in the LGBTQ+ community. Lastly, students reflected on their advisors’ encouragement for open and constructive discourse around the graduate unionization vote, showing a genuine desire to hear about graduate issues.

Baluch shared, “Working with the amazing selection committee was the highlight of my work year. I was so impressed by the thoughtful consideration each nomination received. Selecting the next round of C2C nominees is always a heartwarming experience.” 

“As someone who aspires to be a faculty member someday,” noted Das, “being on the selection committee … was a phenomenal opportunity in understanding the breadth and depth of possibility in how to be a caring mentor in academia.”

She continued, “It was so heartening to hear the different ways that these faculty members are going above and beyond their explicit research and teaching duties and the amazing impact that has made on so many students’ well-being and ability to be successful in graduate school.” 

The Committed to Caring program continues to reinforce MIT’s culture of mentorship, inclusion, and collaboration by recognizing the contributions of outstanding professors. In the coming months, news articles will feature pairs of honorees, and a reception will be held in May.

Share this news article on:

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• Committed to Caring

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• School of Humanities Arts and Social Sciences
• MIT Sloan School of Management
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• Brain and cognitive sciences
• Chemical engineering
• Mechanical engineering
• Nuclear science and engineering
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Related Articles

Fifteen MIT faculty honored as “Committed to Caring” for 2021-23

Twelve MIT faculty honored as “Committed to Caring” for 2020-2021

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Thea Energy

Mechanical engineering intern fall 2024.

• Share This: Share Mechanical Engineering Intern Fall 2024 on Facebook Share Mechanical Engineering Intern Fall 2024 on LinkedIn Share Mechanical Engineering Intern Fall 2024 on X

About Thea Energy:

Thea Energy is leveraging recent breakthroughs in stellarator physics and engineering to create a faster and simpler approach to commercializing fusion energy. The Company is reinventing the stellarator using computer-controlled arrays of planar coils thereby replacing the intricate, complex modular magnets required in all other stellarator architectures. Thea Energy is on a mission to create a limitless source of zero emission energy for a sustainable future.

Fusion Energy Engineering Intern Program:

We are looking for talented technical interns to join our stellar team for the summer or during the school year!

Program Details:

• Summer 12-16 week internship program and/or flexible school year internship
• For school year internships, expected time dedication is flexible with an hourly salary and tailored to your academic schedule

Mechanical Engineering Intern (onsite)

• Mechanical Engineering Interns will develop and exercise their design, analysis, and hands-on skills to support prototyping and stellarator design activities. Activities may include CAD and/or FEA model development, and will culminate in the delivery of functional custom components, tooling, fluid systems, and test equipment. (This role will require at least 3 days onsite per week.)

Manufacturing Engineering Intern (onsite)

• Manufacturing Engineering Interns will support process development, fabrication and assembly, equipment design, and testing for Thea Energy’s HTS magnet prototyping programs. A Manufacturing Engineering intern will be exposed to the physical and strategic aspects of the manufacture of HTS magnets, and will get hands-on experience operating equipment.

Magnet Engineering Intern (onsite)

• Magnet Engineering Interns will support the design, build, testing, and performance analysis of Thea Energy’s custom HTS magnets. Activities may include: design of magnet components and tooling, development of FEA simulations (electromagnetic, mechanical, or thermal), operation of cryogenic tests and test equipment, and development of custom analytical tools to assess magnet performance.

Test Engineering Intern (onsite)

• Test Engineering Interns will support the development and execution of test equipment, facilities, and operations associated with Thea Energy’s custom HTS magnets and magnet-related hardware. To enable test execution and analysis of performance data, this role may include aspects of mechanical, electrical, instrumentation, and software engineering.

Fusion Technology Intern

• Fusion Technology interns will assist scientists and engineers in designing and developing various subsystems for Thea Energy’s stellarator fusion devices.

Plasma Physics Intern

• Plasma Physics interns will work with scientists to model magnetically confined high temperature fusion plasmas using sophisticated computational tools.

Stellarator Optimization Intern

• Stellarator Optimization Interns will support computational physicists and plasma physicists in optimizing stellarator magnetic geometry for Thea Energy’s next-generation fusion devices.

Project assignments are based on existing team needs at the time and may include, but are not limited to:

• High-temperature superconducting magnet engineering, manufacturing, and testing
• Cryogenic and vacuum systems
• Instrumentation and diagnostic systems
• Electrical and control systems engineering
• Mechanical engineering
• Various modeling, simulation, and data analysis roles including but not limited to COMSOL, ANSYS, Python, C++, MATLAB, Simulink, Microsoft Visio, LabVIEW
• Opportunities vary between onsite at our labs in Kearny, NJ and remote
• Candidates will have personalized mentorship directly from technical and management teams

The ideal candidate will have most, if not all, of these requirements:

• Enrolled in a STEM undergraduate or graduate program (mechanical engineering, aerospace engineering, materials science, electrical engineering, etc.)
• Interest in clean and sustainable energy to combat climate change
• Hands-on or computational experience through academic research, club projects, hackathons, or industry internships
• Highly self-motivated, independent, and driven to solve problems
• Authorized to work in the US
• Willingness to learn new things!

It’s not necessary to meet all of the skillsets outlined above. Please feel free to send us a note and tell us why you would be a great fit for a role at Thea Energy.

Diversity and Inclusion:

Thea Energy is an equal opportunity employer committed to creating a company of diverse backgrounds. By creating a diverse environment, we will bring new ideas and approaches to solving some of the world’s hardest (and most important) problems. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, gender, sexual orientation, gender identity or expression, national origin, family or marital status, age, disability, veteran’s status, or other characteristics protected by applicable laws and regulations.

Advertisement

Boston-area students set up encampments to protest war in Gaza

• Willoughby Mariano

Students from several Boston-area colleges have joined a growing national protest following last week's mass arrests and suspensions of pro-Palestinian Columbia University students calling for a cease-fire in Gaza.

About two dozen protesters sat on MIT's Kresge Lawn, huddled over laptops Monday morning, studying in thick coats and blankets. Safiyyah Ogundipe, a senior, said she arrived the night before.

“It seems like there's a really big shift in what people are willing to do, the risks people are willing to take, and we just kind of want to kind of seize on that energy,” said Ogundipe, a protest organizer who is studying chemical engineering.

Demonstrators said they want MIT's administration to cut ties with Israel related to funding and academic projects .

At MIT, the encampment of about a dozen tents was peaceful but the mood was tense. A campus police officer followed Ogundipe from a distance as she spoke to a reporter.

Talia Kahn, president of the MIT Israel Alliance, said protests at other campuses have made Jewish students anxious ahead of Passover observances this evening.

“I have friends at Columbia who were texting me and so scared and I was like, 'God, please don't let that happen at MIT,' ” said Khan, a graduate student studying mechanical engineering.

MIT officials are considering what to do next about the encampment. In a written statement, a spokeswoman said administrators are focused on ensuring the campus is “physically safe and fully functioning."

Student protesters also camped out Sunday night near Emerson College.

The Boston encampments follow a week of chaos at Columbia University after President Minouche Shafik's decision to call in New York police to roust and arrest students. Four of those students have been suspended and barred from their dorm rooms , according to the student-run Columbia Spectator. Shafik's decision came just days after she appeared before a Congressional committee , where she was grilled about instances of antisemitism on campus.

The fallout from the arrests and suspensions was so contentious that administrators shifted classes online this week to ease tensions. Faculty members walked out of class and rallied on campus Monday to oppose Shafik's having called on police.

In Connecticut, the Yale Police Department told NPR 40 to 45 people were arrested at weekend protests. And protests were spreading to other campuses Monday , including at New York University, where police were gathering Monday evening after the administration ordered the protesting students to disperse.

• Columbia University shifts classes to remote-only after a wave of protests on campus

Willoughby Mariano Senior Reporter, Investigations Willoughby Mariano is a senior reporter on WBUR's investigations team.

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