L.C. Evans, Partial Differential Equations, 2nd Edition
640:501 or permission of instructor.
This is the first half of a year-long introductory graduate course on PDEs, and should be useful for students with a variety of research interests: physics and mathematical physics, applied analysis, numerical analysis, differential geometry, complex analysis, and, of course, partial differential equations. The beginning weeks of the course aim to develop enough familiarity and experience with the basic phenomena, approaches, and methods in solving initial/boundary value problems in the contexts of the classical prototype linear PDEs of constant coefficients: the Laplace equation, the D'Alembert wave equation, the heat equation and the Schroedinger equation. A variety of tools and methods, such as Fourier series/eigenfunction expansions, Fourier transforms, energy methods, and maximum principles will be introduced.
Next we will discuss some notions and results that are relevant in treating general PDEs: characteristics, non-characteristic Cauchy problems and Cauchy-Kowalevski theorem, Sobolev spaces, second order elliptic equations.
Schedule of Sections:
Some information about the Fall 2017 semester's offering is posted at here.