MATH 6190: Partial Differential Equations (Fall 2011)

Instructor: Lars Wahlbin

No previous experience with PDE is assumed, but a certain degree of mathematical maturity is.

We shall follow Lawrence C. Evans, PDEs, Part I, "Representation Formulas for Solutions". Apart from a detailed investigation into properties of harmonic functions (Laplace's equation), the heat equation and the wave equation (in their "Ur-forms"), there will be a massive dose of first order nonlinear PDEs. There will also be a grab-bag of special techniques for various interesting special PDEs.

We shall not be able to cover all of Evans's Part I; my estimate is 3/4 of it. What exactly to cut or include will be discussed with the audience.

Text: Lawrence C. Evans, Partial Differential Equations (second edition), Graduate Studies in Mathematics 19, American Mathematical Society, 2010, ISBN 978-0-8218-4974-3.