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# Ordinary Differential Equations

## Module MA2005

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 2021/2 (current)

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 2020SS 2017SS 2012WS 2011/2

### Basic Information

MA2005 is a semester module in German language at Bachelor’s level which is offered in summer semester.

This module description is valid to WS 2021/2.

150 h 45 h 5 CP

### Content, Learning Outcome and Preconditions

#### Content

Basic concepts and elementary methods of integration, vector fields and phase flows on the real line. Non-autonomous equations. Existence, uniqueness and smooth dependence on initial data as well as other parameters for the solutions of general first-order systems. Rectifiability of vector fields near non-singular points. Applications to systems of higher-order. Existence and non-existence for boundary value problems. Integral curves and phase flows of autonomous systems. Linear systems: systems of first-order with constant coefficients (including complex eigenvalues). Stability. Eigenvalue problems (Sturm.Liouville Theorie).

#### Learning Outcome

After successful completion of the modul, students are able to understand and apply the elementary theory of ordinary differential equations, stressing their analytical investigation as well as geometric features of the solutions.

#### Preconditions

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, MA2004 Vector Analysis

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

Please keep in mind that course announcements are regularly only completed in the semester before.

#### Learning and Teaching Methods

lecture, exercise module, presentation

blackboard

#### Literature

V.I. Arnold, Gewöhnliche Differentialgleichungen, 2. Auflage, Springer-Verlag 2001.
W. Walter, Gewöhnliche Differentialgleichungen: eine Einführung, 7. Auflage, Springer-Verlag Berlin 2000.
V.I. Arnold: "Ordinary Differential Equations", translated and edited by RA Silverman - 1973 - MIT Press, Cambridge.

### Module Exam

#### Description of exams and course work

Requirement for successful completion of the modul is to pass a written exam. By the written exam, students prove to know the mathematical concepts and methods of the elementary theory of ordinary differential equations and to be able to apply those to solve mathematical problems from that area.

#### Exam Repetition

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

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