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# Analysis 2

## Module MA1002

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 2015WS 2014/5

### Basic Information

MA1002 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
300 h 105 h 10 CP

### Content, Learning Outcome and Preconditions

#### Content

Power series (in particular disk of convergence and complex exponential function).
Fourier series.
Explicit solutions of simple ordinary differential equations.
Analysis in Rn (differentiation of vector fields and Taylor expansion).
Norms and completeness. Equivalence of norms in Rn.
Open, closed and compact sets in Rn, Bolzano Weierstrass theorem
Banach fixed point theorem for closed subsets of complete normed spaces.
Implicit functions.
Maximization and minimization problems, Lagrange multipliers.
Explicit evaluation of elementary multiple integrals.

#### Learning Outcome

Following the successful completion of the module, students understand the theoretical concepts of real multidimensional analysis and can handled them safely in example situations.

#### Preconditions

MA1001 Analysis 1, MA1101 Linear Algebra und Discrete Structures 1

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 5 Analysis 2 Matthes, D.
Responsible/Coordination: Kreiner, C.
documents
UE 1 Analysis 2 (Supplementary Material) Kreiner, C. Matthes, D.
UE 2 - Kreiner, C.

#### Learning and Teaching Methods

lecture, tutorial, supplement lecture

#### Media

blackboard, assignments

#### Literature

K. Königsberger, Analysis 1, 6. Auflage, Springer 2003.
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 (90 minutes). Students have to give a compressed display of theoretical basics of real multidimensional analysis. They are able to discuss connections with example problems under time pressure.

#### Exam Repetition

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

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