Materials covered include: special relativity, electrodynamics of moving media, waves in dispersive media, microstrip integrated circuits, quantum optics, remote sensing, radiative transfer theory, scattering by rough surfaces, effective permittivities, and random media.
Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.
Introduction to computational techniques for the simulation of a large variety of engineering and engineered systems. Applications drawn from aerospace, mechanical, electrical, and chemical engineering, materials science, and operations research. Topics: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary and partial differential equations; methods for the solution of integral equations; model-order reduction; and Monte Carlo techniques. An introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics.
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; and engineering systems such as finance, traffic flow, and performance analysis of stochastic systems. Computer assignments requiring programming.
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