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Geometric Continuum Mechanics

Module MA5339

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.

Basic Information

MA5339 is a semester module in English language at Master’s level which is offered irregular.

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

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
180 h 60 h 6 CP

Content, Learning Outcome and Preconditions


The lecture course introduces differential geometric concepts and methods which are then used to formulate balance laws and stress theory in an intrinsic, geometric, coordinate- and metric-free fashion. Specific topics include:
1. simplices and uniform fluxes, Cauchy theorem
2. elements of exterior algebra and differentiable manifolds
3. elements of differential forms and integration on manifolds
4. balance principles and fluxes
5. stress theory

Learning Outcome

After successful completion of the module students are able to understand and apply the mathematical theory of differential forms and their integration on manifolds to formulate and study fundamental laws of continuum mechanics in a metric- and coordinate-free framework.


solid knowledge of analysis and linear algebra

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 3 Geometric Continuum Mechanics [MA5339] Karrasch, D. Tue, 10:15–11:45, MI 03.06.011
Thu, 10:15–11:45, MI 02.10.011
Fri, 14:00–16:00, MI 02.06.020

Learning and Teaching Methods

lecture, exercise course
The module is offered as lectures accompanied by irregular practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to the lectures, practice sessions will be offered irregularly. This way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.




- R. Segev, Notes on Metric Independent Analysis of Classical Fields, Mathematical Methods in the Applied Sciences, 36:5 (2013), 497-566.
Further reading:
- M. Epstein, The Geometrical Language of Continuum Mechanics, Cambridge University Press, 2010
- J. M. Lee, Introduction to Smooth Manifolds, Springer, 2012
- T. Aubin, A Course in Differential Geometry, 2001, AMS

Module Exam

Description of exams and course work

oral exam

Exam Repetition

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

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