Complex Analysis

Module MA2006

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
SS 2012WS 2011/2

Basic Information

MA2006 is a semester module in German language at Bachelor’s level which is offered in summer semester.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Introduction to complex analysis: holomorphic functions (complex derivatives, Cauchy-Riemann equations, power series), complex line integrals, Cauchy integral theorem and implications, singularities and residues, conformal maps

Learning Outcome

After successfully attending this course, students are familiar with the basic concepts and results of complex analysis. They also know to apply the calculus of residues.


MA1001 Analysis 1, MA1002 Analysis 2

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Funktionentheorie [MA2006], [MA2008] König, R. Dienstag, 16:00–17:30
UE 1 Übungen zu Funktionentheorie [MA2006], [MA2008] Arnold, C. König, R. Prähofer, M. Dienstag, 17:45–19:00
sowie einzelne oder verschobene Termine
sowie Termine in Gruppen

Learning and Teaching Methods

lecture, exercise module, assignments




K.Jänich, Funktionentheorie, Springer 2008 (6. Auflage) (propaedeutic). R.Remmert, G. Schumacher, Funktionentheorie 1/2, Springer 2002/2007 (5./3. Auflage) (further reading). R. E. Greene, S. G. Krantz, Function theory of one-complex variable, AMS 2006 (3rd edition)

Module Exam

Description of exams and course work

The module examination is based on a written exam (60 minutes). Students have to understand basic concepts of complex analysis and can apply residual calculus.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.