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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 SS 2012

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 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 is included in the following catalogues within the study programs in physics.

  • Further Modules from Other Disciplines
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Basic concepts and elementary methods of integration, vector fields and phase flows on the real line. Existence, uniqueness and smooth dependence on initial data as well as other parameters for the solutions of general systems of non-autonomous first-order equations, phase flows and orbits of systems of autonomous first-order equations, vector fields close to singular as well as non-singular points, first integrals and conservative systems of equations, non-autonomous and autonomous systems of linear first-order equations, variation of constants formula. Application to higher-order equations, boundary-value problems, eigenvalue problems (Sturm-Liouville theory).

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.


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

Learning and Teaching Methods

lecture, exercise module, presentation




V.I. Arnold, Gewöhnliche Differentialgleichungen, 2. Auflage, Springer-Verlag 2001.
W. Walter, Gewöhnliche Differentialgleichungen: eine Einführung, 7. Auflage, Springer-Verlag Berlin 2000.

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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