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Complex Analysis

Module MA2006

This Module is offered by 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

VO 2 Complex Analysis König, R. Tue, 16:00–17:30, MI HS1
UE 1 Complex Analysis (problem sessions) König, R. Prähofer, M. Tue, 17:45–19:00, MI HS3
and 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

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

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

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