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2 097J: Numerical Methods for Partial Differential Equations
3.00 Credits
Massachusetts Institute of Technology
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.
Prerequisite:
Prereq: 18.03 or 18.06
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2 097J - Numerical Methods for Partial Differential Equations
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2 099J: Computational Mechanics of Materials
3.00 Credits
Massachusetts Institute of Technology
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.
Prerequisite:
Prereq: Permission of instructor, programming in either C++, C, or Fortran
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2 099J - Computational Mechanics of Materials
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2 110J: Information, Entropy, and Computation
4.00 Credits
Massachusetts Institute of Technology
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.
Prerequisite:
Prereq: Physics I (GIR)
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2 110J - Information, Entropy, and Computation
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2 111J: Quantum Computation
3.00 Credits
Massachusetts Institute of Technology
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.
Prerequisite:
Prereq: Permission of instructor
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2 111J - Quantum Computation
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2 12: Introduction to Robotics
3.00 Credits
Massachusetts Institute of Technology
Overview of robot mechanisms, dynamics, and intelligent controls. Planar and spatial kinematics, motion planning; mechanism design for manipulators and mobile robots, multi-rigid-body dynamics, 3-D graphic simulation; control design, actuators, sensors; wireless networking, task modeling, human-machine interface, and imbedded software. Weekly laboratories for experience with servo drives, real-time control, and embedded software. Group term project requires design and fabrication of robotic systems.
Prerequisite:
Prereq: 2.004
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2 12 - Introduction to Robotics
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2 131: Advanced Instrumentation and Measurement
3.00 Credits
Massachusetts Institute of Technology
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. No final exam.
Prerequisite:
Prereq: Permission of Instructor
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2 131 - Advanced Instrumentation and Measurement
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2 14: Analysis and Design of Feedback Control Systems
3.00 Credits
Massachusetts Institute of Technology
No course description available.
Prerequisite:
Prereq: 2.004
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2 14 - Analysis and Design of Feedback Control Systems
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2 140: Analysis and Design of Feedback Control Systems
3.00 Credits
Massachusetts Institute of Technology
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.
Prerequisite:
Prereq: 2.004 or permission of instructor
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2 140 - Analysis and Design of Feedback Control Systems
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2 141: Modeling and Simulation of Dynamic Systems
3.00 Credits
Massachusetts Institute of Technology
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.
Prerequisite:
Prereq: 2.151
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2 141 - Modeling and Simulation of Dynamic Systems
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2 151: Advanced System Dynamics and Control
4.00 Credits
Massachusetts Institute of Technology
Analytical and graphical 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. Emphasis on application of techniques to physical systems.
Prerequisite:
Prereq: 2.004, 18.06
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2 151 - Advanced System Dynamics and Control
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