Fully nonlinear first-order PDEs, shocks, eikonal equations. Classification of second-order linear equations: elliptic, parabolic, hyperbolic. Well-posed problems. Laplace and Poisson equations; Gauss’s theorem, Green’s function. Existence and uniqueness theorems (Sobolev spaces methods, Perron’s method). Applications to irrotational flow, elasticity, electrostatics, etc. Heat equation, existence and uniqueness theorems, Green’s function, special solutions. Wave equation and vibrations. Huygens’ principle. Spherical means. Retarded potentials. Water waves and various approximations, dispersion relations. Symmetric hyperbolic systems and waves. Maxwell equations, Helmholtz equation, Schrödinger equation. Radiation conditions. Gas dynamics. Riemann invariants. Shocks, Riemann problem. Local existence theory for general symmetric hyperbolic systems. Global existence and uniqueness for the inviscid Burgers’ equation. Integral equations, single- and double-layer potentials. Fredholm theory. Navier-Stokes equations. Stokes flow, Reynolds number. Potential flow; connection with complex variables. Blasius formulae. Boundary layers. Subsonic, supersonic, and transonic flow. Instructor: Bruno.
Score: 6.3095536 Details | Listing | Web page
Finite difference and finite volume methods for hyperbolic problems. Stability and error analysis of nonoscillatory numerical schemes: i) linear convection: Lax equivalence theorem, consistency, stability, convergence, truncation error, CFL condition, Fourier stability analysis, von Neumann condition, maximum principle, amplitude and phase errors, group velocity, modified equation analysis, Fourier and eigenvalue stability of systems, spectra and pseudospectra of nonnormal matrices, Kreiss matrix theorem, boundary condition analysis, group velocity and GKS normal mode analysis; ii) conservation laws: weak solutions, entropy conditions, Riemann problems, shocks, contacts, rarefactions, discrete conservation, Lax-Wendroff theorem, Godunov’s method, Roe’s linearization, TVD schemes, high-resolution schemes, flux and slope limiters, systems and multiple dimensions, characteristic boundary conditions; iii) adjoint equations: sensitivity analysis, boundary conditions, optimal shape design, error analysis. Interface problems, level set methods for multiphase flows, boundary integral methods, fast summation algorithms, stability issues. Spectral methods: Fourier spectral methods on infinite and periodic domains. Chebyshev spectral methods on finite domains. Spectral element methods and h-p refinement. Multiscale finite element methods for elliptic problems with multiscale coefficients. Not offered 2008–09.
Score: 6.3095536 Details | Listing | Web page
Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations, Chernoff bounds. Instructor: Owhadi.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
A seminar course in applied and computational mathematics. Weekly lectures on current developments are presented by staff members, graduate students, and visiting scientists and engineers. Graded pass/fail only.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
For course description, see Civil Engineering.
Score: 6.3095536 Details | Listing | Web page
Topics include linear spaces, operators and matrices, integral equations, variational principles, ordinary and partial differential equations, stability, perturbation theory. Applications to problems in engineering and science are stressed. Instructor: Beck.
Score: 6.3095536 Details | Listing | Web page
Variational principles and Lagrange’s equations. Response of mechanical systems to periodic, transient, and random excitation. Free and forced response of discrete and continuous systems. Approximate analysis methods. Introduction to nonlinear oscillation theory and stability. Not offered 2008–09.
Score: 6.3095536 Details | Listing | Web page
Fundamental concepts and equations of elasticity. Linearized theory of elastostatics and elastodynamics: basic theorems and special solutions. Finite theory of elasticity: constitutive theory, semi-inverse methods. Variational methods. Applications to problems of current interest. Not offered 2008–09.
Score: 6.3095536 Details | Listing | Web page
By arrangement with members of the staff, properly qualified graduate students are directed in independent studies in mechanics.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
For course description, see Aeronautics.
Score: 6.3095536 Details | Listing | Web page
Research in the field of applied mechanics. By arrangement with members of the staff, properly qualified graduate students are directed in research.
Score: 6.3095536 Details | Listing | Web page
For course description, see Chemistry.
Score: 6.3095536 Details | Listing | Web page
Introduction to solid-state electronics, including physical modeling and device fabrication. Topics: semiconductor crystal growth and device fabrication technology, carrier modeling, doping, generation and recombination, pn junction diodes, MOS capacitor and MOS transistor operation, and deviations from ideal behavior. Laboratory includes computer-aided layout, and fabrication and testing of light-emitting diodes, transistors, and inverters. Students learn photolithography, and use of vacuum systems, furnaces, and device-testing equipment. Instructor: Scherer.
Score: 6.3095536 Details | Listing | Web page
Introduction to the use of thermodynamics and statistical mechanics in physics and engineering. Entropy, temperature, and the principal laws of thermodynamics. Canonical equations of state. Applications to cycles, engines, phase and chemical equilibria. Probability and stochastic processes. Kinetic theory of perfect gases. Statistical mechanics. Applications to gases, gas degeneration, equilibrium radiation, and simple solids. Instructors: Vahala, Crosignani.
Score: 6.3095536 Details | Listing | Web page
This course cover fundamentals of optics with emphasis on modern optical applications, intended to exhibit basic optical phenomena including interference, dispersion, birefringence, diffraction, and laser oscillation, and the applications of these phenom-ena in optical systems employing two-beam and multiple-beam interferometry, Fourier-transform image processing, holography, electro-optic modulation, and optical detection and heterodyning. System examples to be selected from optical communications, radar, and adaptive optical systems. Instructor: Staff.
Score: 6.3095536 Details | Listing | Web page
Laboratory experiments to acquaint students with the contemporary aspects of modern optical research and technology. Experiments encompass many of the topics and concepts covered in APh 23. Instructor: Staff.
Score: 6.3095536 Details | Listing | Web page
Selected experiments chosen to familiarize students with laboratory equipment, procedures, and characteristic phenomena in plasmas, fluid turbulence, fiber optics, X-ray diffraction, microwaves, high-temperature superconductivity, black-body radiation, holography, and computer interfacing of experiments. Instructor: Bellan.
Score: 6.3095536 Details | Listing | Web page
Supervised experimental research experience, open only to senior-class applied physics majors. Requirements will be set by individual faculty members, but will include a written report based upon actual laboratory experience. The selection of topic and the final report must be approved by the Applied Physics Undergraduate Committee. Students desiring additional units should register in APh 100. Not offered on a pass/fail basis. Instructor: Staff.
Score: 6.3095536 Details | Listing | Web page
Supervised theoretical research experience, open only to senior-class applied physics majors. Requirements will be set by individual faculty members, but will include a written report based upon actual laboratory experience. The selection of topic and the final report must be approved by the Applied Physics Undergraduate Committee. Not offered on a pass/fail basis. This course cannot be used to satisfy the laboratory requirement in APh. Instructor: Staff.
Score: 6.3095536 Details | Listing | Web page
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