Inhalt:

• vector spaces, norms, principal axis theorem

• Banach spaces, Hilbert spaces

• Sobolev spaces

• theory of elliptic differential equations

• Fourier transformation

• distributions

Lernziele und Kompetenzen:

Students learn advanced methods in linear algebra and basic concepts of functional analysis. Furthermore, students learn applications in solving partial differential equations. The course teaches abstract mathematical structures. 

Literatur:

• Lehrbuch: Dobrowolski, Angewandte Funktionalanalysis, Springer 2006.