Partial Differential Equations MATH 718 (3)

First-order linear equations, the method of characteristics. The wave equation. Harmonic functions, the maximum principle, Green's functions. The heat equation. Distributions and transforms. Higher dimensional eigenvalue problems. An introduction to nonlinear equations. Burgers' equation and shock waves. Students may not take a 700-division course if it is being offered in conjunction with a 400-division course which they have taken previously.