This entry is from Summer semester 2018 and might be obsolete. You can find a current equivalent here.

# Complex Analysis (dt. Funktionentheorie (Analytische Funktionen einer komplexen Veränderlichen))

 Level, degree of commitment Advanced module, compulsory elective module Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) Credit points,formal requirements 9 CP Course requirement(s): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Duration,frequency One semester, irregular Person in charge of the module's outline Prof. Dr. Thomas Bauer

## Contents

• Complex differentiability, Cauchy-Riemann differential equations
• Power series, Taylor expansion
• Curve integrals, Cauchy's integral theorems
• Isolated singularities, elementary holomorphic functions, meromorphic functions, Laurent series
• Residue theorem and applications
• Conform maps, Möbius group
• Normal families, Montel's theorem
• Riemann mapping theorem

## Qualification Goals

The students shall

• understand how complex-analytical methods help to solve real-analytical problems,
• deepen their understanding of the elementary functions through the complex viewpoint,
• learn about the connections between methods of geometry, algebra, and analysis, as well as topology and number theory, and thus develop their mathematical understanding,
• Learn methods and skills that are central to applications in computer science (e.g. coding theory), physics (e.g. quantum theory) and engineering (e.g. electrical engineering)
• practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstraction, proof methods),
• improve their oral communication skills in the recitation class by practicing free speech in front of an audience and during discussion.

## Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen Analysis und Lineare Algebra vermittelt werden.

## Applicability

This module is an export-only module, and can as such only be used in other study programs, not in B.Sc. Mathematics.

• Fischer,W., Lieb, I.: Funktionentheorie: Komplexe Analysis in einer Veränderlichen, Vieweg; Conway, J.B.: Functions of one complex variable, Graduate Texts in Mathematics, Springer; Lang, S.: Complex analysis, Graduate Texts in Mathematics, Springer; Remmert, R., Schumacher, G.: Funktionentheorie I,II, Berlin: Springer

This page describes a module according to the latest valid module guide in Summer semester 2018. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.