Math 819: Partial Differential Equations

Course content: In this course we will study some basic partial differential equations with an emphasis on nonlinear equations, or at least nonlinear methods. My plan is to cover the following topics (roughly Evans' chapters 2, 3, 5, 6 and perhaps a little of 10):
 
(1) Laplace, heat and wave equations
(2) Nonlinear first-order equations via characteristics
(3) Scalar conservation laws
(4) Hamilton-Jacobi equations
(5) Sobolev spaces
(6) Existence, uniqueness, and regularity for general second-order elliptic equations