Modul

The module will be completed by an oral exam (about 30 min).

At the end of the course, students can

• explain the basic concepts and results of the theory of infinite products and apply them in examples within the framework of Weierstrass's theorems
• reproduce the Mittag-Leffler theorem and derive conclusions from it
• explain Riemann's mapping theorem and are able to describe what Montel's theorem is and how this theorem is included in the proof of Riemann's theorem
• name the most important properties of class S of simple functions and formulate the (proven) Bieberbach conjecture
• can explain the basic concepts of the theory of harmonic functions and apply them in examples
• explain the Schwarz reflection principle.
• describe properties of regular and singular points in power series and discuss them with examples.

None

• infinite products
• Mittag-Leffler's theorem
• Montel's theorem
• Riemann's mapping theorem
• conformal mappings
• univalent (schlicht) functions
• automorphisms of some domains
• harmonic functions
• Schwarz reflection principle
• regular and singular points of power series

Basics of complex analysis, for example from the “Analysis 4” module, are recommended.

Total workload: 240 hours

Attendance: 90 hours

• lectures, problem classes, and examination

Self-studies: 150 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination