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# 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 SS 2020

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 2020/1SS 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
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

#### Learning and Teaching Methods

lecture, exercise module, assignments

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
TimeLocationInfoRegistration
Complex Analysis
Fri, 2021-07-23, 11:30 till 12:30 Beachten Sie die Informationen zur Prüfungsteilnahme während der COVID-19-Pandemie unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/. // See https://www.tum.de/en/about-tum/news/coronavirus/coronavirus-exams/ for further information on exams during the COVID-19 pandemic. till 2021-06-30 (cancelation of registration till 2021-07-16)
Thu, 2021-10-07, 14:15 till 15:15 Beachten Sie die Informationen zur Prüfungsteilnahme während der COVID-19-Pandemie unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/. // See https://www.tum.de/en/about-tum/news/coronavirus/coronavirus-exams/ for further information on exams during the COVID-19 pandemic. till 2021-09-27 (cancelation of registration till 2021-09-30)
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