Topics in functional analysis and applications

Distributions: Test Functions and Distributions on iir Derivatives of Distributions, Convolutions, Tempered Distributions Sobolev Spaces: Domains in iir, Extension Operators, Inclusion Theorems, Compactness Theorems, Trace Theory Weak Solutions of Elliptic Problems: The Lax- Milgram Lemma and Variations Examples of Elliptic Problems, Regularity of Weak Solutions, Elementary Theory of the Finite Element Method Semi-Groups and Applications: Unbounded Operators on a Banach Space, Co-Semigroups, Applications to the Wave Equation, The Inhomogeneous Equation Appendix 1: The Topology on D Appendix 2: Vector-Valued Integration.