18.306 Advanced Partial Differential Equations with Applications, Spring 2004
Name
18-306Spring2004/OcwWeb/Mathematics/18-306Spring2004/CourseHome/index.htm
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14.54 KB
Format
HTML
Checksum (MD5)
28532166c34a45fb3889d69aa11191a2
Author(s)
Margetis, Dionisios
Alternative Title
Advanced Partial Differential Equations with Applications
Date Issued
June 2004
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.
Subjects
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Persistent DSpace Link
