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# Analysis 1

## Module MA1001

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 2014/5

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 2021WS 2020/1SS 2020SS 2015WS 2014/5

### Basic Information

MA1001 is a semester module in German language at Bachelor’s level which is offered in winter 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

Basic proof techniques including mathematical induction. Basic notions and calculus rules for functions and sets including inverse functions. Trigonometric and exponential functions (tied to the viewpoint of G8) and their inverses as examples.
Real numbers (axiomatic, not derived from Q, field axioms are assumed to be given from the linear algebra course), in particular the notion of supremum and the completeness axiom.
Complex numbers. Notion of limit, convergence of sequences.
Series: Convergence, absolute convergence, quotient criterion.
Analysis of a function of a single variable: Continuity, derivative and integral (calculus and notions), Taylor expansion including those of trigonometric and exponential functions.
Uniform convergence.

#### Learning Outcome

Having successfully completed this module, the students have computational skills, graphical perception and theoretical understanding of functions of a single variable.

#### Preconditions

knowledge of natural numbers, integers and rational numbers

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

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

#### 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 show their possession of a descriptive imagination and theoretical understanding of functions of one real variable. They are able to deal with trigonometric and exponential functions and they show their numeracy skills with real and complex numbers in limited time.

#### Exam Repetition

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

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