Functional and Numerical Analysis (FOMICS block course)

This course provides a concise introduction to some prominent subjects in functional analysis theory and some applications to the analysis and numerical solution of partial differential equations (PDEs). Starting from Banach spaces and basic topological considerations, we will consider linear and bounded operators and dual spaces, as well as some classical fixed-point results. We then will introduce Hilbert spaces, scalar products, and the Lax-Milgram theorem. On the PDE side, we will introduce the Lebesgue integral, Sobolev-spaces, and Galerkin discretization for linear elliptic PDEs.