This course will be an introduction to methods of functional analysis that are widely used in current research. We will begin with the Hill-Yoshida Theorem on generators of semigroups that solve evolution equations, and shall cover spaces of distributions, some harmonic analysis, and methods of the calculus of variations, all will applications to PDE's, linear and non-linear, of current interest.
Analysis, 2nd edition, by Lieb and Loss
507 or 501 and permission of the instructor. (The course will be accessible to my current 501 students.)