Einführung in die Funktionalanalysis (BV/COME)

What it is about

You will learn the fundamental concepts and structures of functional analysis for real and complex function spaces (metric, norm, inner product space, classical function spaces, linear mappings). Building on that, you will cover topological concepts such as convergence, continuity and completeness and apply the theory to boundary value problems (Sobolev spaces, variational formulation, Galerkin method). In the end you will understand the mathematical foundations of the finite element method and be able to use function spaces as abstractions of familiar linear and analytical objects.

What you will be able to do

• Understand fundamental concepts of functional analysis
• Apply structures such as normed and inner product spaces
• Explain topological properties: convergence, continuity, completeness
• Understand Sobolev spaces and variational formulation of boundary value problems
• Understand Galerkin approach and basics of the finite element method

What the module consists of

• Vorlesung (2 SWS)Conveying theoretical concepts and numerous examples
• Übungsstunde (1 SWS)Discussion and deepening through exercises

Teaching method

• VorlesungIntroduction and explanation of the theory as well as examples
• ÜbungenApplying and deepening the lecture content through exercises