Math 704: Methods of Applied Mathematics-2

Fabian Waleffe

Spring 2009 Spring 2004 Spring 2003 Spring 2002 Spring 2001

Kelvin's ship wave pattern

(From "Why are special functions special?" Physics Today, Apr 2001)

Photo by Ensign John Gay, US Navy, somewhere over the Pacific between Hawaii and Japan, July 7, 1999.

BOOM!: An example of transition from ELLIPTIC to HYPERBOLIC PDEs

Catalog Description

Derivation, nature and solution of canonical partial differential equations of applied mathematics. Conservation laws, advection, diffusion. First order PDEs, characteristics, shocks. Traffic flow, eikonal and Hamilton-Jacobi equations. Higher order PDEs: Classification, Fourier analysis, well-posedness. Series solutions and integral transforms. Green's functions and distributions. Similarity solutions. Asymptotics of Fourier integrals. Laplace's method, stationary phase. Ship waves. Perturbation methods.



More abstract references: