Math 819: Partial Differential Equations

This is an introductory course in partial differential
equations. We will follow the textbook by L. C. Evans.

The course will consist of the following parts:
1. Basic properties of solutions of Laplace's equation and the heat and wave equations.
2. Second order linear elliptic and parabolic equations: existence, regularity, maximum principles.
3. First order nonlinear PDE: introduction to Hamilton-Jacobi equations and conservation laws.