In 6.635, topics covered include: special relativity, electrodynamics of moving media, waves …
In 6.635, topics 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, random media, Green's functions for planarly layered media, integral equations in electromagnetics, method of moments, time domain method of moments, EM waves in periodic structures: photonic crystals and negative refraction.
This course emphasizes concepts and techniques for solving integral equations from an …
This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.
6.336J is an introduction to computational techniques for the simulation of a …
6.336J is 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. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5211 (Introduction to Numerical Simulation).
A presentation of the fundamentals of modern numerical techniques for a wide …
A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).
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