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 2021/2	SS 2020	SS 2019	SS 2012	WS 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 workload	Contact hours	Credits (ECTS)
150 h	45 h	5 CP

Content, Learning Outcome and Preconditions

Content

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.

Preconditions

MA1001 Analysis 1, MA1002 Analysis 2
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

SS 2022 SS 2021 SS 2020 SS 2019 SS 2018 SS 2017 SS 2016 SS 2015 SS 2014 SS 2013 SS 2012 SS 2011 SS 2010

Type	SWS	Title	Lecturer(s)	Dates	Links
VO	2	Complex Analysis	Wolf, M.	Tue, 16:00–17:30, MI HS1 and singular or moved dates	documents
TT	1	Complex Analysis (problem sessions)	Prähofer, M. Wolf, M.	singular or moved dates and dates in groups	eLearning current

Learning and Teaching Methods

lecture, exercise module, assignments

Media

blackboard

Literature

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.

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.

Title
Time	Location	Info	Registration
Complex Analysis
	0001
	101