This course is a continuation of Math 16:640:517 (Partial Differential Equations I.) The course provides an introduction to hyperbolic and dispersive partial differential equations. The primary goal of the course is to provide students with a solid understanding of the well-posedness theory (existence, uniqueness, regularity and development of singularities) for solutions of the initial value problem of the evolution equations arising in mathematical physics, such as equations of D'Alembert, Euler, Maxwell, Klein-Gordon, Schroedinger, and Dirac, as well as Einstein's equations of general relativity. Familiarity with basic material covered in Math 517, such as Holder and Sobolev spaces, Sobolev embeddings, and L^2 elliptic regularity theory, is assumed. No physics background is needed for this course.
Math 16:640:517 or permission of instructor