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Course 2: Mechanical Engineering
Fall 2024


First-Year Introductory Subjects

2.00A Designing for the Future: Earth, Sea, and Space
______

Undergrad (Spring)
Prereq: Calculus I (GIR) and Physics I (GIR)
Units: 3-3-3
______
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.
Staff

2.00B Toy Product Design
______

Undergrad (Spring)
Not offered regularly; consult department
Prereq: None
Units: 3-5-1
______
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.
Staff

2.S00 Special Subject in Mechanical Engineering
______

Undergrad (Spring) Can be repeated for credit; second half of term
Prereq: None
Units arranged
______
Lecture, seminar, or laboratory subject consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 
Staff

2.S01 Special Subject in Mechanical Engineering
______

Undergrad (Spring); second half of term
Prereq: None
Units arranged
______
Lecture, seminar, or laboratory subject consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter. 
Staff

2.S02 Special Subject in Mechanical Engineering
______

Undergrad (Spring)
Prereq: None
Units arranged
______
Lecture, seminar, or laboratory subject consisting of material not offered in regularly scheduled subjects. Can be repeated for credit only for completely different subject matter.
Staff

2.00C[J] Design for Complex Environmental Issues
______

Undergrad (Spring)
(Same subject as 1.016[J], EC.746[J])
Prereq: None
Units: 3-1-5
______
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, S. L. Hsu, J. Grimm

Core Undergraduate Subjects

2.00 Introduction to Design
______

Undergrad (Fall, Spring); second half of term
Prereq: None
Units: 2-2-2
Add to schedule Lecture: MW3.30-5 (BEGINS OCT 21) (3-370) Lab: R9.30-12.30 (BEGINS OCT 21) (1-307) or TBA or TBA
______
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.
Fall: M. Yang
Spring: Staff
No textbook information available

2.000 Explorations in Mechanical Engineering
______

Undergrad (Spring)
Not offered regularly; consult department
Prereq: None
Units: 2-0-0 [P/D/F]
______
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.
Staff

2.001 Mechanics and Materials I
______

Undergrad (Fall, Spring) Rest Elec in Sci & Tech
Prereq: Physics I (GIR); Coreq: 2.087 or 18.03
Units: 4-1-7
Add to schedule Lecture: TR10.30-12.30 (10-250) Recitation: R1.30-3 (1-307) or R3-4.30 (1-307) or R EVE (7-8.30 PM) (1-307) or F9.30-11 (1-307) or F11-12.30 (1-307) or F12.30-2 (1-307) or F2-3.30 (1-307) or F3.30-5 (1-307) +final
______
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.
D. Parks, M. Guo
No textbook information available

2.002 Mechanics and Materials II
______

Undergrad (Spring)
Prereq: Chemistry (GIR) and 2.001
Units: 3-3-6
______
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.
Staff

2.003[J] Dynamics and Control I
______

Undergrad (Fall, Spring) Rest Elec in Sci & Tech
(Same subject as 1.053[J])
Prereq: Physics II (GIR); Coreq: 2.087 or 18.03
Units: 4-1-7
Add to schedule Lecture: TR9-10.30 (10-250) Recitation: R12 (1-371) or R1 (3-442) or R2 (3-442) or F10 (5-217) or F11 (5-217) or F12 (5-217) +final
______
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.
Fall: T. Peacock
Spring: T. Sapsis, N. Makris
No textbook information available

2.004 Dynamics and Control II
______

Undergrad (Fall, Spring)
Prereq: Physics II (GIR) and 2.003
Units: 4-2-6
Add to schedule Lecture: TR9.30-11 (3-270) Lab: M1-3 (3-062B) or M3-5 (3-062B) or T1-3 (3-062B) or T3-5 (3-062B) Recitation: R3 (3-270) or F11 (3-270)
______
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.
Fall: F. Hover
Spring: F. Hover
No textbook information available

2.005 Thermal-Fluids Engineering I
______

Undergrad (Fall, Spring)
Prereq: (Physics II (GIR), 18.03, and (2.086, 6.100B, or 18.06)) or permission of instructor
Units: 5-0-7
Add to schedule Lecture: MW9-11 (1-190) Recitation: R2 (1-371) or R3 (1-246) or R4 (1-246) or F10 (1-246) or F11 (1-246) or F1 (1-246) +final
______
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.
Fall: P. Lermusiaux
Spring: J. Buongiorno, K. Varanasi
No textbook information available

2.006 Thermal-Fluids Engineering II
______

Undergrad (Fall, Spring)
Prereq: 2.005
Units: 5-0-7
Add to schedule Lecture: MW9.30-11,F9 (3-370) Recitation: F1 (1-371) or F2 (1-371) +final
______
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.
Fall: R. Karnik
Spring: S. Deng, J. Brisson
Textbooks (Fall 2024)

2.007 Design and Manufacturing I
______

Undergrad (Spring)
Prereq: 2.001 and 2.670; Coreq: 2.086
Units: 3-4-5
______
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
______

Undergrad (Fall, Spring) Partial Lab
Prereq: 2.007; or Coreq: 2.017 and (2.005 or 2.051)
Units: 3-3-6
Add to schedule Lecture: W2-5 (35-225) Lab: M2-5 (35-125) or T9-12 (35-125) or T2-5 (35-125) or W9-12 (35-125) or R9-12 (35-125) or R2-5 (35-125)
______
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.
Fall: K. Becker
Spring: J.-H. Chun, J. Ramos
No textbook information available

2.009 The Product Engineering Process
______

Undergrad (Fall)
Prereq: 2.001, 2.003, (2.005 or 2.051), and (2.00B, 2.670, or 2.678)
Units: 3-3-9
Add to schedule Lecture: MWF1 (10-250) Lab: T2-5 (3-037A) or T2-5 (3-037C) or T2-5 (3-037D) or T EVE (7-10 PM) (3-037A) or T EVE (7-10 PM) (3-037B) or W2-5 (3-037A) or W2-5 (3-037C) or W2-5 (3-037D) or W9-12 (3-037A) or W2-5 (3-037B) or W EVE (7-10 PM) (3-037A) or W EVE (7-10 PM) (3-037B) or R9-12 (3-037A) or R9-12 (3-037B) or R2-5 (3-037A) or R2-5 (3-037B) or T2-5 (3-037B)
______
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.
D. Wallace
No textbook information available

2.013 Engineering Systems Design
______

Undergrad (Fall)
(Subject meets with 2.733)
Prereq: (2.001, 2.003, (2.005 or 2.051), and (2.00B, 2.670, or 2.678)) or permission of instructor
Units: 0-6-6
Add to schedule Lecture: TR2.30-5 (NE45-202A)
______
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.
D. Hart
No required or recommended textbooks

2.014 Engineering Systems Development
______

Undergrad (Spring) Can be repeated for credit
(Subject meets with 2.734)
Prereq: (2.001, 2.003, (2.005 or 2.051), and (2.00B, 2.670, or 2.678)) or permission of instructor
Units: 0-6-6
______
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.
Staff

2.016 Hydrodynamics
______

Undergrad (Fall)
Prereq: 2.005
Units: 3-0-9
Add to schedule Lecture: TR11-12.30 (3-442)
______
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. Techet
No textbook information available

2.017[J] Design of Electromechanical Robotic Systems
______

Undergrad (Spring) Partial Lab
(Same subject as 1.015[J])
Prereq: 2.003, 2.016, and 2.678; Coreq: 2.671
Units: 3-3-6
______
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, T. Consi

2.019 Design of Ocean Systems
______

Undergrad (Spring)
Prereq: 2.001, 2.003, and (2.005 or 2.016)
Units: 3-3-6
______
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.
Staff

2.086 Numerical Computation for Mechanical Engineers
______

Undergrad (Fall, Spring) Rest Elec in Sci & Tech
Prereq: Calculus II (GIR) and Physics I (GIR); Coreq: 2.087 or 18.03
Units: 2-2-8
Add to schedule Lecture: MW12 (3-270) Lab: W2.30-4.30 (3-442) or R9-11 (5-134) or R2.30-4.30 (35-310) or F9-11 (5-134) +final
______
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.
Fall: F. Hover
Spring: D. Frey
No required or recommended textbooks

2.087 Engineering Mathematics: Linear Algebra and ODEs
______

Undergrad (Fall); first half of term
Not offered regularly; consult department
Prereq: Calculus II (GIR) and Physics I (GIR)
Units: 2-0-4
______
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.
Staff

Dynamics and Acoustics

2.032 Dynamics
______

Graduate (Fall)
Prereq: 2.003
Units: 4-0-8
Add to schedule Lecture: MW1-2.30 (1-150) Recitation: T4 (1-371)
______
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. Akylas
No textbook information available

2.033[J] Nonlinear Dynamics and Turbulence
______

Not offered academic year 2025-2026Graduate (Spring)
(Same subject as 1.686[J], 18.358[J])
(Subject meets with 1.068)
Prereq: 1.060A
Units: 3-2-7
______
Reviews theoretical notions of nonlinear dynamics, instabilities, and waves with applications in fluid dynamics. Discusses hydrodynamic instabilities leading to flow destabilization and transition to turbulence. Focuses on physical turbulence and mixing from homogeneous isotropic turbulence. Also covers topics such as rotating and stratified flows as they arise in the environment, wave-turbulence, and point source turbulent flows. Laboratory activities integrate theoretical concepts covered in lectures and problem sets. Students taking graduate version complete additional assignments.
L. Bourouiba

2.034[J] Nonlinear Dynamics and Waves
______

Not offered academic year 2024-2025Graduate (Spring)
(Same subject as 1.685[J], 18.377[J])
Prereq: Permission of instructor
Units: 3-0-9
______
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.
Staff

2.036[J] Nonlinear Dynamics and Chaos
______

Not offered academic year 2024-2025Graduate (Spring)
(Same subject as 18.385[J])
Prereq: 18.03 or 18.032
Units: 3-0-9
______
Introduction to the theory of nonlinear dynamical systems with applications from science and engineering. Local and global existence of solutions, dependence on initial data and parameters. Elementary bifurcations, normal forms. Phase plane, limit cycles, relaxation oscillations, Poincare-Bendixson theory. Floquet theory. Poincare maps. Averaging. Near-equilibrium dynamics. Synchronization. Introduction to chaos. Universality. Strange attractors. Lorenz and Rossler systems. Hamiltonian dynamics and KAM theory. Uses MATLAB computing environment.
Staff

2.050[J] Nonlinear Dynamics: Chaos
______

Undergrad (Fall)
(Same subject as 12.006[J], 18.353[J])
Prereq: Physics II (GIR) and (18.03 or 18.032)
Units: 3-0-9
Add to schedule Lecture: TR9.30-11 (2-131)
______
Introduction to nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial conditions and strange attractors. Lorenz attractor. Period doubling, intermittency, and quasiperiodicity. Scaling and universality. Analysis of experimental data: Fourier transforms, Poincare sections, fractal dimension, and Lyapunov exponents. Applications to mechanical systems, fluid dynamics, physics, geophysics, and chemistry. See 12.207J/18.354J for Nonlinear Dynamics: Continuum Systems.
R. Rosales
Textbooks (Fall 2024)

2.060[J] Structural Dynamics
______

Not offered academic year 2024-2025Graduate (Fall)
(Same subject as 1.581[J], 16.221[J])
(Subject meets with 1.058)
Prereq: 18.03 or permission of instructor
Units: 3-1-8
______
Examines response of structures to dynamic excitation: free vibration, harmonic loads, pulses and earthquakes. Covers systems of single- and multiple-degree-of-freedom, up to the continuum limit, by exact and approximate methods. Includes applications to buildings, ships, aircraft and offshore structures. Students taking graduate version complete additional assignments.
T. Cohen

2.062[J] Wave Propagation
______

Graduate (Spring)
Not offered regularly; consult department
(Same subject as 1.138[J], 18.376[J])
Prereq: 2.003 and 18.075
Units: 3-0-9
______
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
______

Undergrad (Spring)
(Subject meets with 2.066)
Prereq: 2.003, 6.3000, 8.03, or 16.003
Units: 3-0-9
______
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.
Staff

2.066 Acoustics and Sensing
______

Graduate (Spring)
(Subject meets with 2.065)
Prereq: 2.003, 6.3000, 8.03, 16.003, or permission of instructor
Units: 3-0-9
______
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.
N. C. Makris

Solid Mechanics and Materials

2.071 Mechanics of Solid Materials
______

Graduate (Spring)
Prereq: 2.002
Units: 4-0-8
______
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.
Staff

2.072 Mechanics of Continuous Media
______

Graduate (Fall)
Not offered regularly; consult department
Prereq: 2.071
Units: 3-0-9
______
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.
L. Anand

2.073 Solid Mechanics: Plasticity and Inelastic Deformation
______

Graduate (Fall)
Prereq: 2.071
Units: 3-0-9
Add to schedule Lecture: MW2.30-4 (5-134)
______
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.
L. Anand
No textbook information available

2.074 Solid Mechanics: Elasticity
______

Graduate (Fall)
Prereq: 2.002 and 18.03
Units: 3-0-9
Add to schedule Lecture: MW11-12.30 (1-150) Recitation: F11 (5-134) +final
______
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
No textbook information available

2.075 Mechanics of Soft Materials
______

Graduate (Fall)
Prereq: None
Units: 3-0-9
Add to schedule Lecture: MW11-12.30 (1-371)
______
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.
X. Zhao
Textbooks (Fall 2024)

2.076[J] Mechanics of Heterogeneous Materials
______

Not offered academic year 2024-2025Graduate (Fall)
(Same subject as 16.223[J])
Prereq: 2.002, 3.032, 16.20, or permission of instructor
Units: 3-0-9
______
Mechanical behavior of heterogeneous materials such as thin-film microelectro- mechanical systems (MEMS) materials and advanced filamentary composites, with particular emphasis on laminated structural configurations. Anisotropic and crystallographic elasticity formulations. Structure, properties and mechanics of constituents such as films, substrates, active materials, fibers, and matrices including nano- and micro-scale constituents. Effective properties from constituent properties. Classical laminated plate theory for modeling structural behavior including extrinsic and intrinsic strains and stresses such as environmental effects. Introduction to buckling of plates and nonlinear (deformations) plate theory. Other issues in modeling heterogeneous materials such as fracture/failure of laminated structures.
B. L. Wardle, S-G. Kim

2.077 Solid Mechanics: Coupled Theories
______

Not offered academic year 2024-2025Graduate (Fall)
Prereq: 2.072
Units: 3-0-9
______
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.
Staff

2.080[J] Structural Mechanics
______

Graduate (Fall)
(Same subject as 1.573[J])
Prereq: 2.002
Units: 4-0-8
Add to schedule Lecture: MW2.30-4 (2-105) Recitation: F9 (5-217)
______
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.
D. Parks
No textbook information available

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

Graduate (Spring)
(Same subject as 16.230[J])
Prereq: 2.071, 2.080, or permission of instructor
Units: 3-1-8
______
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.
W. M. van Rees

2.082 Ship Structural Analysis and Design
______

Graduate (Spring); second half of term
Prereq: 2.081 and 2.701
Units: 3-0-3
______
Design application of analysis developed in 2.081J. 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.
Staff

2.083[J] Topology Optimization of Structures
(New)
______

Not offered academic year 2025-2026Graduate (Fall)
(Same subject as 1.583[J], 16.215[J])
Prereq: None
Units: 3-0-9
Add to schedule Lecture: MW1-2.30 (5-233)
______
Covers free-form topology design of structures using formal optimization methods and mathematical programs, including design of structural systems, mechanisms, and material architectures. Strong emphasis on designing with gradient-based optimizers, finite element methods, and design problems governed by structural mechanics. Incorporates optimization theory and computational mechanics fundamentals, problem formulation, sensitivity analysis; and introduces cutting-edge extensions, including to other and multiple physics. 
J. Carstensen
No textbook information available

Computational Engineering

2.0911[J] Computational Design and Fabrication
______

Undergrad (Spring)
(Same subject as 6.4420[J])
(Subject meets with 6.8420)
Prereq: Calculus II (GIR) and (6.1010 or permission of instructor)
Units: 3-0-9
______
Introduces computational aspects of computer-aided design and manufacturing. Explores relevant methods in the context of additive manufacturing (e.g., 3D printing). Topics include computer graphics (geometry modeling, solid modeling, procedural modeling), physically-based simulation (kinematics, finite element method), 3D scanning/geometry processing, and an overview of 3D fabrication methods. Exposes students to the latest research in computational fabrication. Students taking the graduate version complete additional assignments.
W. Matusik

2.095 Introduction to Finite Element Methods
______

Not offered academic year 2025-2026Undergrad (Spring)
(Subject meets with 2.098)
Prereq: 2.086 or permission of instructor
Units: 3-0-9
______
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.
A. Patera

2.096[J] Introduction to Modeling and Simulation
______

Graduate (Fall)
(Same subject as 6.7300[J], 16.910[J])
Prereq: 18.03 or 18.06
Units: 3-6-3
Add to schedule Lecture: MW1-2.30 (32-155)
______
Introduction to computational techniques for modeling and simulation of a variety of large and complex engineering, science, and socio-economical systems. Prepares students for practical use and development of computational engineering in their own research and future work. Topics include mathematical formulations (e.g., automatic assembly of constitutive and conservation principles); linear system solvers (sparse and iterative); nonlinear solvers (Newton and homotopy); ordinary, time-periodic and partial differential equation solvers; and model order reduction. Students develop their own models and simulators for self-proposed applications, with an emphasis on creativity, teamwork, and communication. Prior basic linear algebra required and at least one numerical programming language (e.g., MATLAB, Julia, Python, etc.) helpful.
L. Daniel
No required or recommended textbooks

2.097[J] Numerical Methods for Partial Differential Equations
______

Graduate (Fall)
(Same subject as 6.7330[J], 16.920[J])
Prereq: 18.03 or 18.06
Units: 3-0-9
Add to schedule Lecture: MW9.30-11 (37-212)
______
Covers the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential and integral equations. Topics include mathematical formulations; finite difference, finite volume, finite element, and boundary element discretization methods; and direct and iterative solution techniques. The methodologies described form the foundation for computational approaches to engineering systems involving heat transfer, solid mechanics, fluid dynamics, and electromagnetics. Computer assignments requiring programming.
J. Peraire
No textbook information available

2.098 Introduction to Finite Element Methods
______

Graduate (Spring)
Not offered regularly; consult department
(Subject meets with 2.095)
Prereq: 2.086 or permission of instructor
Units: 3-0-9
______
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.
A. Patera

2.099[J] Computational Mechanics of Materials
______

Not offered academic year 2025-2026Graduate (Spring)
(Same subject as 16.225[J])
Prereq: Permission of instructor
Units: 3-0-9
______
Formulation of numerical (finite element) methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered includes finite deformation elasticity and inelasticity. Numerical formulation and algorithms include variational formulation and variational constitutive updates; finite element discretization; constrained problems; time discretization and convergence analysis. Strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science are stressed throughout. Experience in either C++, C, or Fortran required.
R. Radovitzky

System Dynamics and Control

2.110 Information, Entropy, and Computation
______

Undergrad (Fall)
Not offered regularly; consult department
Prereq: Physics I (GIR)
Units: 3-0-6
______
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.
S. Lloyd

2.111[J] Quantum Computation
______

Graduate (Fall)
(Same subject as 6.6410[J], 8.370[J], 18.435[J])
Prereq: 8.05, 18.06, 18.700, 18.701, or 18.C06
Units: 3-0-9
Add to schedule Lecture: MWF1 (4-370) +final
______
Provides an introduction to the theory and practice of quantum computation. Topics covered: physics of information processing; quantum algorithms including the factoring algorithm and Grover's search algorithm; quantum error correction; quantum communication and cryptography. Knowledge of quantum mechanics helpful but not required.
P. Shor
Textbooks (Fall 2024)

2.12 Introduction to Robotics
______

Undergrad (Spring)
(Subject meets with 2.120)
Prereq: 2.004
Units: 3-2-7
______
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.
H. Asada

2.120 Introduction to Robotics
______

Graduate (Spring)
(Subject meets with 2.12)
Prereq: 2.004 or permission of instructor
Units: 3-2-7
______
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.
H. Asada

2.121 Stochastic Systems
______

Undergrad (Spring)
(Subject meets with 2.122, 2.22)
Prereq: None. Coreq: 2.004
Units: 3-0-9
______
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.
T.P. Sapsis

2.122 Stochastic Systems
______

Graduate (Spring)
(Subject meets with 2.121, 2.22)
Prereq: 2.004 and 2.087
Units: 4-0-8
______
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.
T. P. Sapsis

2.124[J] Robotics: Science and Systems
______

Undergrad (Spring) Institute Lab
(Same subject as 6.4200[J], 16.405[J])
Prereq: ((1.00 or 6.100A) and (2.003, 6.1010, 6.1210, or 16.06)) or permission of instructor
Units: 2-6-4
______
Presents concepts, principles, and algorithmic foundations for robots and autonomous vehicles operating in the physical world. Topics include sensing, kinematics and dynamics, state estimation, computer vision, perception, learning, control, motion planning, and embedded system development. Students design and implement advanced algorithms on complex robotic platforms capable of agile autonomous navigation and real-time interaction with the physical word. Students engage in extensive written and oral communication exercises. Enrollment limited.
Staff

2.131 Advanced Instrumentation and Measurement
______

Graduate (Spring)
Prereq: Permission of instructor
Units: 3-6-3
______
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

2.132 Instrumentation and Measurement: MICA Projects
(New)
______

Undergrad (Fall)
(Subject meets with 2.133)
Prereq: 2.671 or permission of instructor
Units: 3-6-3
Add to schedule Lecture: TR12.30-2 (3-149)
______
Engages students in project-based learning by using a wide variety of experimental setups called MICA (Measurement, Instrumentation, Control, and Analysis) Workstations to learn about sensors, actuators, instrumentation, and measurement techniques. Over 50 MICA Workstations allow experiments to be performed on a broad range of phenomena including those found in optics, electronics, acoustics, biology, botany, material science, mechanics, thermal, and fluid systems. Experiments utilize Mathematica Notebooks in which students conduct data analysis and model fitting, and complete homework assignments. The integration of ChatGPT into Mathematica provides help in the learning process. Students also build new Workstations guided by CAD models and develop the Mathematica code to run experiments, perform data analyses, and model parameter estimation. Students taking graduate version build more sophisticated Workstations..
I. Hunter
No textbook information available

2.133 Instrumentation and Measurement: MICA Projects
(New)
______

Graduate (Fall)
(Subject meets with 2.132)
Prereq: Permission of instructor
Units: 3-6-3
Add to schedule Lecture: TR12.30-2 (3-149)
______
Engages students in project-based learning by using a wide variety of experimental setups called MICA (Measurement, Instrumentation, Control, and Analysis) Workstations to learn about sensors, actuators, instrumentation, and measurement techniques. Over 50 MICA Workstations allow experiments to be performed on a broad range of phenomena including those found in optics, electronics, acoustics, biology, botany, material science, mechanics, thermal, and fluid systems. Experiments utilize Mathematica Notebooks in which students conduct data analysis and model fitting, and complete homework assignments. The integration of ChatGPT into Mathematica provides help in the learning process. Students also build new Workstations guided by CAD models and develop the Mathematica code to run experiments, perform data analyses, and model parameter estimation. Students taking graduate version build more sophisticated Workstations.
I. Hunter
No textbook information available

2.14 Analysis and Design of Feedback Control Systems
______

Undergrad (Spring)
(Subject meets with 2.140)
Prereq: 2.004
Units: 3-3-6
______
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.
Staff

2.140 Analysis and Design of Feedback Control Systems
______

Graduate (Spring)
(Subject meets with 2.14)
Prereq: 2.004 or permission of instructor
Units: 3-3-6
______
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.L. Trumper

2.141 Modeling and Simulation of Dynamic Systems
______

Graduate (Fall)
Not offered regularly; consult department
Prereq: Permission of instructor
Units: 3-0-9
______
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.
N. Hogan

2.145 Design of Compliant Mechanisms, Machines and Systems
______

Undergrad (Fall)
(Subject meets with 2.147)
Prereq: 2.003 and 2.007
Units: 3-3-6
Add to schedule Lecture: MW11-12.30 (35-308) Lab: W2-5 (1-132)
______
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
No textbook information available

2.147 Design of Compliant Mechanisms, Machines and Systems
______

Graduate (Fall)
(Subject meets with 2.145)
Prereq: 2.003 and 2.007
Units: 3-3-6
Add to schedule Lecture: MW11-12.30 (35-308) Lab: W2-5 (1-132)
______
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.
M. Culpepper
No textbook information available

2.151 Advanced System Dynamics and Control
______

Graduate (Fall)
Prereq: 2.004 and (2.087 or 18.06)
Units: 4-0-8
Add to schedule Lecture: TR1-2.30 (3-370) Recitation: W4 (1-190)
______
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.
N. Hogan
No textbook information available

2.152[J] Nonlinear Control
______

Graduate (Spring)
(Same subject as 9.110[J])
Prereq: 2.151, 6.7100, 16.31, or permission of instructor
Units: 3-0-9
______
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.
Staff

2.153 Adaptive Control and Connections to Machine Learning
______

Not offered academic year 2024-2025Graduate (Fall)
Prereq: 2.151
Units: 3-0-9
______
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
______

Graduate (Fall)
Prereq: 2.22
Units: 3-0-9
Add to schedule Lecture: TR9.30-11 (1-134)
______
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.
N. Patrikalakis
No textbook information available

2.155 Artificial Intelligence and Machine Learning for Engineering Design
______

Undergrad (Fall)
(Subject meets with 2.156)
Prereq: 2.086, 6.100A, or permission of instructor
Units: 3-0-9
Add to schedule Lecture: MW1-2.30 (1-190)
______
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. 
F. Ahmed
No textbook information available

2.156 Artificial Intelligence and Machine Learning for Engineering Design
______

Graduate (Fall)
(Subject meets with 2.155)
Prereq: None
Units: 3-0-9
Add to schedule Lecture: MW1-2.30 (1-190)
______
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.
F. Ahmed
No textbook information available

2.16 Learning Machines
______

Undergrad (Spring)
Not offered regularly; consult department
(Subject meets with 2.168)
Prereq: 2.086, 18.075, and (6.3700 or 18.05)
Units: 4-0-8
______
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.
Staff

2.160 Identification, Estimation, and Learning
______

Graduate (Fall)
Prereq: 2.151, 6.7100, 16.31, or permission of instructor
Units: 3-0-9
Add to schedule Lecture: MW1-2.30 (5-134)
______
Provides a broad theoretical basis for estimation, identification, and learning of linear and nonlinear systems at the cross-disciplinary area of system dynamics and control, machine learning, and statistics. Recursive least squares estimate, partial least squares, Kalman filter and extended Kalman filter, Bayes filter and particle filter; parametric and non-parametric system identification, Wiener-Hopf equation, persistent excitation, unbiased estimates, asymptotic variance, experiment design; function approximation theory, neural nets, radial basis functions, Koopman operator for exact linearization of nonlinear systems, and dynamic mode decomposition. Context-oriented mini-projects: robotics, self-driving cars, biomedical engineering, wearable sensors.
H. Asada
No textbook information available

2.165[J] Robotics
______

Graduate (Fall)
(Same subject as 9.175[J])
Prereq: 2.151 or permission of instructor
Units: 3-0-9
Add to schedule Lecture: TR1-2.30 (5-217)
______
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 Slotine
No textbook information available

2.168 Learning Machines
______

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

2.171 Analysis and Design of Digital Control Systems
______

Graduate (Fall)
Prereq: 2.14, 2.151, or permission of instructor
Units: 3-3-6
Add to schedule Lecture: MW2.30-4 (1-379) Lab: T2-5 (3-004)
______
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
No textbook information available

2.174[J] Advancing Mechanics and Materials via Machine Learning
______

Graduate (Spring)
(Same subject as 1.121[J])
(Subject meets with 1.052)
Prereq: Permission of instructor
Units: 3-0-9
______
Concepts in mechanics (solid mechanics: continuum, micro, meso, and molecular mechanics; elasticity, plasticity, fracture and buckling) and machine learning (stochastic optimization, neural networks, convolutional neural nets, adversarial neural nets, graph neural nets, recurrent neural networks and long/short-term memory nets, attention models, variational/autoencoders) introduced and applied to mechanics problems. Covers numerical methods, data and image processing, dataset generation, curation and collection, and experimental validation using additive manufacturing. Modules cover: foundations, fracture mechanics and size effects, molecular mechanics and applications to biomaterials (proteins), forward and inverse problems, mechanics of architected materials, and time dependent mechanical phenomena. Students taking graduate version complete additional assignments.
M. Buehler

2.177[J] Designing Virtual Worlds
______

Undergrad (Fall)
(Same subject as CMS.342[J])
(Subject meets with 2.178[J], CMS.942[J])
Prereq: None
Units: 4-2-6 [P/D/F]
Add to schedule Lecture: F1.30-4.30 (3-370)
______
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.
K. Zolot
No textbook information available

2.178[J] Designing Virtual Worlds
______

Graduate (Fall)
(Same subject as CMS.942[J])
(Subject meets with 2.177[J], CMS.342[J])
Prereq: None
Units: 4-2-6 [P/D/F]
Add to schedule Lecture: F1.30-4.30 (3-370)
______
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.
K. Zolot
No textbook information available

2.18 Biomolecular Feedback Systems
______

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

2.180 Biomolecular Feedback Systems
______

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

2.183[J] Biomechanics and Neural Control of Movement
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Graduate (Spring)
(Same subject as 9.34[J])
(Subject meets with 2.184)
Prereq: 2.004 or permission of instructor
Units: 3-0-9
______
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.
N. Hogan

2.184 Biomechanics and Neural Control of Movement
______

Undergrad (Spring)
(Subject meets with 2.183[J], 9.34[J])
Prereq: 2.004 or permission of instructor
Units: 3-0-9
______
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.
Staff


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