This entry is from Winter semester 2018/19 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

Module imported from B.Sc. Mathematics.

It can be attended at FB12 in study program(s)

• LAaG Mathematics

When studying LAaG Mathematics, this module can be attended in the study area Advanced Modules.

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Reinen Mathematics zugeordnet ist.