This will be a basic Functional Analysis course covering the three major theorems, the Hahn-Banach theorem, Uniform boundedness principle and the Open mapping-Closed Graph theorem. We shall also do Fredholm theory as it is useful to people doing PDE and also the Spectral theory of self-adjoint and bounded operators. The course will emphasize applications of Functional Analysis to PDE via illustrations in the use of Sobolev spaces.
Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haim Brezis, Universitext, Springer-Verlag
501, 502