Prof. Dr. Robert Denk

  • Time: Tuesday 10.00-11.30 in R 512, Thursday 11.45-13.15 in F 420
  • Registration and lecture notes in ILIAS

Content
Lecture notes
Related modules
Exams

Content:

This lecture gives an introduction into fundamental questions and methods of functional analysis. It is suited for students with interest in applied analysis (both from mathematics and from mathematical finance, but also for physicist).
Main topics of functional analysis are vector spaces with infinite dimension and linear mappings between them (linear operators). The related theorems analyse the underlying structures and give deeper insight in the spaces as well as in the operators. The results are important for many areas of mathematics and physics, for instance for the theory of partial differential equations, mathematical physics and numerical mathematics.
Topics of the lectures are, among others, normed spaces and Hilbert spaces, dual spaces, Hahn-Banach theorems, uniform boundedness principle and bounded and unbounded operators and their spectral decomposition.

The lecture is adapted for students in the 4th semester or higher.

The lecture is similar to the corresponding chapters in the book

R. Denk, R. Racke: Kompendium der Analysis - Ein kompletter Bachelor-Kurs von Reellen Zahlen zu Partiellen Differentialgleichungen Band 2. Springer Spektrum, Wiesbaden 2012, 305 Seiten.

Further references are announced in the lecture.

Lecture notes:

The lecture notes will be written in parallel to the course and can be found in ILIAS.

Related modules:

Mathematik (88105H):
- Bachelor Ergänzungsmodul Funktionalanalysis (6530)
- Master Wahlmodul (3100)
- Diplomstudiengang: Hauptstudium Vorlesungen
- GymPO 2009: Wahlmodul (3100)
- WPO 2001: Hauptstudium Vorlesungen

Master Gymnasiales Lehramt Physik (85128H):
- Wahlpflichtveranstaltung (2610)

First part of the lecture:
Mathematische Finanzökonomie (82776H) - neue PO ab SS 2011:
- Wahlbereich 7101: Lehrveranstaltungen aus dem Fachbereich Mathematik und Statistik
3100 MFÖ-BA-Modul 3: Aufbaumodul Analysis
Mathematik 2200 Funktionalanalysis

Exams:

  • To pass this module successfully, you have to solve a sufficiently large part of the exercises (approximately 50%) and take part actively in the exercise groups.
  • The first written exam will probably take place on August 22, 2017, the second written exam on October 9, 2017  (both for the first half of the semester and for the whole semester). The written exam is part of the module.