MATH 6190: Partial Differential Equations (Fall 2009)

Instructor: Alexander Vladimirsky

We will mostly follow Partial Differential Equations by L.C. Evans. I intend to cover in detail representation formulas for linear PDEs [Chapter 2] and the basic theory for first-order non-linear equations (starting with the method of characteristics and concentrating on Hamilton-Jacobi PDEs and conservation laws) [Chapter 3]. We will also discuss assorted topics from Chapter 4 (similarity solutions, transform methods, asymptotics, power series), Chapter 8 (calculus of variations), and/or Chapter 10 (control theoretic interpretation of Hamilton-Jacobi PDEs).