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# Analysis 2

## Module MA0002

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 2019/20

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 2020WS 2019/20

### Basic Information

MA0002 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
270 h 135 h 9 CP

### Content, Learning Outcome and Preconditions

#### Content

- Analysis im Rn (Differentiation für Vektorfelder inklusive Taylorentwicklung)
- Grundlegende Begriffe der Topologie
- Kurvenintegral, Grundbegriffe der Vektoranalysis: Gradient, Divergenz, Rotation
- Fixpunktsatz von Banach für abgeschlossene Teilmengen vollständig normierter Räume
- Implizite Funktionen
- Maximums- und Minimumsprobleme inklusive Lagrangesche Multiplikatorregel
- Lösungstheorie gewöhnlicher Differentialgleichungen
- Lineare Systeme
- Fourierreihen stückweiser stetiger periodischer Funktionen

#### Learning Outcome

Nach dem erfolgreichen Abschluss des Moduls besitzen die Studierenden ein theoretisches Verständnis der Grundbegriffe der reellen Analysis im Mehrdimensionalen (z.B. Differentiation im Mehrdimensionalen) sowie über zentrale Sätze (z.B. Satz über implizite Funktionen, Banach'scher Fixpunktsatz) und haben Theorie und Verfahren zur Lösung von Differentialgleichungen erlernt. Sie sind in der Lage die erlernten Theorien, Methoden und Verfahren in Beispielsituationen sicher anzuwenden und mit diesen Zusammenhänge herzustellen.

#### Preconditions

MA0001 Analysis 1, MA0004 Linear Algebra 1

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 5 Analysis 2 [MA0002] Friesecke, G. Kruse, H. Tue, 10:15–11:45, virtuell
Wed, 11:30–12:15, virtuell
Fri, 10:15–11:45, virtuell
eLearning
UE 2 Analysis 2 (Exercise Session) [MA0002] Friesecke, G. Kruse, H.
Assistants: Steinert, M.Vögler, D.
dates in groups
UE 2 Analysis 2 (Central Exercise Session) [MA0002] Friesecke, G. Kruse, H. Mon, 16:00–18:00, virtuell

#### Learning and Teaching Methods

lecture,exercise module

#### Media

blackboard, assignments

#### Literature

K. Königsberger, Analysis 2, 6. Auflage, Springer 2004.
W. Rudin, Principles of Mathematical Analysis, 2nd ed, McGraw Hill, 1964.

### Module Exam

#### Description of exams and course work

The module examination is based on a written exam (120 minutes).

#### Exam Repetition

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

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