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# Elementary Differential Geometry

## Module MA2204

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.

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
SS 2012WS 2011/2

### Basic Information

MA2204 is a semester module in German language at Bachelor’s level which is offered in summer semester.

This module description is valid to SS 2021.

150 h 45 h 5 CP

### Content, Learning Outcome and Preconditions

#### Content

Grundlagen der Differentialgeometrie von Kurven und Flächen in der Ebene und im Raum. Krümmungsbegriffe in Ebene und Raum. Vierscheitelsatz, Torsion, Tangentialraum, kovariante Richtungsableitungen, geodätische Linien, Krümmungsgrößen. Ausblicke auf höhere Dimensionen, Riemannsche Mannigfaltigkeiten, Minimalflächen.

#### Learning Outcome

Nach dem erfolgreichen Abschluss des Moduls ist der Studierende in der Lage, gekrümmte Objekte in der Ebene und im Raum sowie im Ansatz auch gekrümmte Räume mit analytischen Methoden zu behandeln.

#### Preconditions

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2, MA2203 Algebraic Structures in Geometry

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.

blackboard

#### Literature

W. Kühnel: Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten, 4. Auflage, Vieweg, 2008, ISBN: 3834804118.
M. P. do Carmo: Differentialgeometrie von Kurven und Flächen, Vieweg, 1983.

### Module Exam

#### Description of exams and course work

The module examination is based on a written exam (60 minutes).

#### Exam Repetition

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

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