Math 704: Spring 2002

Methods of Applied Mathematics-2

Fabian Waleffe

Day  Time  Place 
TR  9:30-10:45pm B223 Van Vleck Hall

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.

Outline

Grading

Two in-class exams, at least two take-homes. NO FINAL. Exams will be: Thursday March 21 and Tuesday May 7.

Office hours:

By appointment

Suggested Problems

Problem Set 1 Due Thur Mar 14, 2002

References

Less applied references (some would say `purer')