704 - Methods of Applied Mathematics II | Department of Mathematics, University of Wisconsin

Instructor:

George Craciun

Time and Place:

TR 1:00 pm-2:15 pm

textbooks:

"Partial Differential Equations: Analytical Solution Techniques" 2nd edition, by J. Kevorkian

Course Content:

Derivation, nature, and solution of canonical partial differential equations (PDE) of applied mathematics. Linear PDE: advection equation, Laplace's equation (elliptic), heat equation (parabolic), wave equation (hyperbolic). Nonlinear PDE: Hamilton-Jacobi equations, conservation laws (Burgers' equation, shallow water equations, compressible fluid flow). Solution techniques: separation of variables, Fourier transform, characteristics, Green's functions, similarity solutions, asymptotics.