University of Illinois at Urbana-Champaign

Math 553 Partial Differential Equations

Professor Richard S. Laugesen, Fall 2007

Eigenfunction of the Laplacian on an L-shaped region. (The Mathworks.)

The course begins with the method of characteristics for first-order equations and then proceeds to examine the famous second-order partial differential equations of mathematical physics, namely the heat (or diffusion), wave and Laplace equations. The focus is initially on finding formulas for solutions, but then moves to the qualitative theory: how do solutions change as the initial and/or boundary data changes, what is the speed of propagation of the solutions, how does the energy behave as time passes, and so on. Also, how do these features differ between the three classical equations?