Geometric Continuum Mechanics
Module MA5339
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 workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 180 h | 60 h | 6 CP |
Content, Learning Outcome and Preconditions
Content
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
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.
Preconditions
solid knowledge of analysis and linear algebra
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| 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 |
eLearning |
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.
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.
Media
blackboard
Literature
- 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
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