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# Analysis 1

## Module MA0001

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 2020/1

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 2020WS 2019/20

### Basic Information

MA0001 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
270 h 135 h 9 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. Explicit solutions of simple ordinary differential equations.

#### Learning Outcome

Nach dem erfolgreichen Abschluss des Moduls besitzen die Studierenden Rechenfertigkeiten im Reellen und Komplexen. Sie verfügen über eine anschauliche Vorstellung und ein theoretisches Verständnis von Funktionen einer reellen Veränderlichen. Sie kennen Grundbegriffe (z.B. Grenzwert, Stetigkeit, Ableitung, Integral) und grundlegende Methoden (z.B. Bestimmung des Konvergenzverhaltens von Reihen, Taylorapproximation, Separationsmethode zur Lösung einfacher Differentialgleichungen) der Analysis und sind in der Lage, die erworbenen Kenntnisse erfolgreich auf einfache Problemstellungen anzuwenden.

#### Preconditions

knowledge of natural numbers, integers and rational numbers

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 5 Analysis 1 [MA0001] Friesecke, G. Kruse, H. Tue, 12:00–13:30, MI HS1
Mon, 14:15–15:45, MI HS1
Fri, 08:30–10:00, Interims I 101
and singular or moved dates
eLearning
UE 2 Analysis 1 (Exercise Session) [MA0001] Friesecke, G. Kruse, H. dates in groups
UE 2 Analysis 1 (Central Exercise Session) [MA0001] Friesecke, G. Kruse, H. Mon, 12:15–13:45, PH HS1

#### Learning and Teaching Methods

lecture, exercise module

#### 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).

#### 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
Analysis 1
Thu, 2022-02-24, 8:00 till 10:00 Bitte beachten Sie die Hinweise unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/. // Please read the information at https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/ carefully. till 2022-01-15 (cancelation of registration till 2022-02-17)
Thu, 2022-04-14, 14:15 till 16:15 Bitte beachten Sie die Hinweise unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/. // Please read the information at https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/ carefully. till 2022-04-04 (cancelation of registration till 2022-04-07)
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