de | en

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 2021/2 (current)

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

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2021/2SS 2020SS 2019SS 2012WS 2011/2

Basic Information

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

This Module is included in the following catalogues within the study programs in physics.

  • Further Modules from Other Disciplines
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
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Please keep in mind that course announcements are regularly only completed in the semester before.

VO 2 Complex Analysis Wolf, M. Tue, 16:00–17:30, MI HS1
and singular or moved dates
TT 1 Complex Analysis (problem sessions) Prähofer, M. Wolf, M. singular or moved dates
and dates in groups

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

Aktueller Hinweis angesichts des eingeschränkten Präsenzbetriebs auf Grund der CoViD19-Pandemie: Die Prüfungsform ändert sich gemäß §13a APSO auf das Prüfungsformat: einmalige Übungsleistung.
In dieser wird überprüft, inwieweit die Studierenden die grundlegenden Konzepte der Funktionentheorie verstanden haben sowie den Residuenkalkül anwenden können. In einer schriftlichen Prüfung wird das Verständnis der in den Lehrveranstaltungen behandelten Themen durch Kurzfragen und Anwendung auf verschiedene Problemstellungen abgeprüft. Dabei werden vor allem Rechenbeispiele im Stil der Übungsaufgaben herangezogen.

Exam Repetition

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Complex Analysis
Thu, 2021-10-07, 14:15 till 15:15 Einmalige Übungsleistung till 2021-09-27 (cancelation of registration till 2021-09-30)
Top of page