Math 704: Spring 2004

Fabian Waleffe

Day	Time	Place
TR	9:30-10:45pm	B305 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.

Grading

Two in-class exams, one or two take-homes. NO FINAL. Exams: TBA

Take-home due May 11

Office hours:

By appointment

References

Partial Differential Equations of Applied Mathematics, Erich Zauderer, 2nd Ed., Wiley-Interscience 1989. [Graduate, Textbook]
Elementary Applied Partial Differential Equations, Richard Haberman, THIRD Edition, Prentice-Hall 1998. [Undergrad-Grad Textbook, Separation, Green's functions background, Chap 12-14: graduate applied Math]
Linear and Nonlinear waves , G.B. Whitham, Wiley 1974. [Research Monograph, a classic]
Similarity, Self-Similarity and Intermediate Asymptotics, G.I. Barenblatt, Cambridge [Research Monograph]

More abstract references:

Partial Differential Equations , F. John, Springer-Verlag, 4th edition, 1986. [Chaps 1, 2]
Partial Differential Equations , L.C. Evans, American Mathematical Society 1999. [Chaps 1-4, Textbook for Math 819, not applied]
Partial Differential Equations , R. McOwen, Prentice-Hall 1996. [Not applied math, but nice concise overview]