Topics covered include an introduction to the theory of distributions, topology of test functions, convolutions, Schwartz space, tempered distributions, Paley-Wiener theorem, Fourier transform and Sobolev spaces (definitions, extension operators, continuum and compact imbeddings, trace results), elliptic boundary value problems (variational formulation, weak solutions, maximum principle, regularity results).

Suggested texts:

1. 1. 1. 1. 1. Barros-Nato, An Introduction to the Theory of Distributions, Marcel Dekker Inc., New York, 1973.
            2. Kesavan S., Topics in Functional Analysis and Applications, Wiley Eastern Ltd., 1989.
            3. L. C. Evans, Partial Differential Equations, University of California, Berkeley, 1998.
            4. Haim Brezis, Functional Analysis, Sobolev Spaces, and Partial Differential Equations.