18.306 Advanced Partial Differential Equations with Applications, Spring 2004

Margetis, Dionisios

Author(s)

Margetis, Dionisios

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Alternative title

Advanced Partial Differential Equations with Applications

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Abstract

A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.

Date issued

2004-06

URI

http://hdl.handle.net/1721.1/56302

Department

Massachusetts Institute of Technology. Department of Mathematics

Other identifiers

18.306-Spring2004

local: 18.306

local: IMSCP-MD5-69c946018adbaeba7014e807b79f34c3

Keywords

partial differential equations (pde), nonlinear pde, Diffusion, dispersion, Initial and boundary value problems, Characteristics and shocks, Separation of variables, transform methods, Green's functions, Asymptotics, geometrical theory, Dimensional analysis, self-similarity, traveling waves, Singular perturbation and boundary layers, Solitons, Variational methods, Free-boundary problems, fluid dynamics, electrical engineering, mechanical engineering, materials science, quantum mechanics

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Mathematics (18) - Archived