Complex Function Theory 2

What it is about

You deal with the continuation of holomorphic functions, meromorphic functions on the Riemann sphere, and fundamental constructions in function theory (infinite products, Weierstrass and Mittag-Leffler theorems). You will also learn descriptive Riemann surfaces, homology and holomorphic differential forms, and apply the Riemann mapping theorem. In the end you will be able to construct holomorphic or meromorphic functions with prescribed zeros/poles and practically use the Riemann mapping.

What you will be able to do

• Compute holomorphic continuation of real-valued functions
• Understand meromorphic functions on the Riemann sphere
• Construct holomorphic and meromorphic functions with given zeros and poles
• Grasp the concept of Riemann surfaces
• Understand basic concepts of homology and holomorphic differential forms
• Apply the Riemann Mapping Theorem

What the module consists of

• VorlesungDelivery of content in lectures with illustrative examples and discussion
• ÜbungProblem sheets and solutions for self-check and deepening of lecture content

Teaching method

• VorlesungExplains the theory, motivates independent engagement and study of literature
• ÜbungEnables practical application of lecture content through exercises and solutions
• TafelarbeitDemonstration of calculation steps and proofs during the lecture