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  • 18 330: Introduction to Numerical Analysis

    3.00 Credits
    Massachusetts Institute of Technology

    Basic techniques for the efficient numerical solution of problems in science and engineering. Root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra. Knowledge of programming in Fortran, C, or MATLAB helpful. Prerequisite:    Prereq: Calculus II (GIR); 18.03 or 18.034
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  • 18 335J: Introduction to Numerical Methods

    3.00 Credits
    Massachusetts Institute of Technology

    Advanced introduction to numerical linear algebra and related numerical methods. Topics include direct and iterative methods for linear systems, eigenvalue and QR/SVD factorizations, stability and accuracy, floating-point arithmetic, sparse matrices, preconditioning, and the memory considerations underlying modern linear algebra software. Starting from iterative methods for linear systems, explores more general techniques for local and global nonlinear optimization, including quasi-Newton methods, trust regions, branch-and-bound, and multistart algorithms. Also addresses Chebyshev approximation and FFTs. MATLAB is introduced for problem sets. Prerequisite:    Prereq: 18.03 or 18.034; 18.06, 18,700, or 18.701
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  • 18 336J: Fast Methods for Partial Differential and Integral Equations

    3.00 Credits
    Massachusetts Institute of Technology

    Unified introduction to the theory and practice of modern, near linear-time, numerical methods for large-scale partial-differential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterfly-based methods; multiresolution approaches, such as multigrid algorithms and hierarchical low-rank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging. Prerequisite:    Prereq: 6.336, 16.920, 18.085, 18.335, or permission of instructor
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  • 18 337J: Parallel Computing

    3.00 Credits
    Massachusetts Institute of Technology

    Advanced interdisciplinary introduction to modern scientific computing on parallel supercomputers. Numerical topics include dense and sparse linear algebra, N-body problems, and Fourier transforms. Geometrical topics include partitioning and mesh generation. Other topics include architectures and software systems with emphasis on understanding the realities and myths of what is possible on the world's fastest machines. Prerequisite:    Prereq: 18.06, 18.700, or 18.701
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  • 18 338: Eigenvalues of Random Matrices

    3.00 Credits
    Massachusetts Institute of Technology

    Covers the modern main results of random matrix theory as it is currently applied in engineering and science. Topics include matrix calculus for finite and infinite matrices (e.g., Wigner's semi-circle and Marcenko-Pastur laws), free probability, random graphs, combinatorial methods, matrix statistics, stochastic operators, passage to the continuum limit, moment methods, and compressed sensing. Knowledge of MATLAB hepful, but not required. Prerequisite:    Prereq: 18.701 or permission of instructor
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  • 18 353J: Nonlinear Dynamics I: Chaos

    3.00 Credits
    Massachusetts Institute of Technology

    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 II. Prerequisite:    Prereq: 18.03 or 18.034; Physics II (GIR)
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  • 18 354J: Nonlinear Dynamics II: Continuum Systems

    3.00 Credits
    Massachusetts Institute of Technology

    General mathematical principles of continuum systems. (1) From microscopic to macroscopic. Examples range from random walkers, to Newtonian mechanics, to option pricing. (2) Singular Perturbations. Examples include boundary layer theory, snow flakes and geophysical flows. (3) Instability. Generalize ideas from 18.353 to continuum systems. Examples from fluid mechanics, solid mechanics, astrophysics and biology. (4) Pattern formation and turbulence. Prerequisite:    Prereq: 18.353 or permission of instructor
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  • 18 355: Fluid Mechanics

    3.00 Credits
    Massachusetts Institute of Technology

    Topics include the development of Navier-Stokes equations, ideal flows, boundary layers, lubrication theory, Stokes flows, and surface tension. Fundamental concepts illustrated through problems drawn from a variety of areas including geophysics, bilocomotion and the dynamics of sport. Particular emphasis is given to the interplay between dimensional analysis, scaling arguments and rigorous theory. Course material supplemented by classroom and laboratory demonstrations. Prerequisite:    Prereq: 18.354, 12.800, or 2.25
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  • 18 357: Interfacial Phenomena

    3.00 Credits
    Massachusetts Institute of Technology

    Covers fluid systems dominated by the influence of interfacial tension. The roles of curvature pressure and Marangoni stress are elucidated in a variety of fluid systems. Particular attention given to drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics. Theoretical developments accompanied by classroom demonstrations. Highlights the role of surface tension in biology. Prerequisite:    Prereq: 18.354, 18.355, 12.800, or 2.25
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  • 18 369: Mathematical Methods in Nanophotonics

    3.00 Credits
    Massachusetts Institute of Technology

    High-level approaches to understanding complex optical media, structured on the scale of the wavelength, that are not generally analytically soluable. The basis for understanding optical phenomena such as photonic crystals and band gaps, anomalous diffraction, mechanisms for optical confinement, optical fibers (new and old), nonlinearities, and integrated optical devices. Methods covered include linear algebra and eigensystems for Maxwell's equations, symmetry groups and representation theory, Bloch's theorem, numerical eigensolver methods, time and frequency-domain computation, perturbation theory, and coupled-mode theories. Prerequisite:    Prereq: 18.305 or permission of instructor
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