Differential Forms
Module MA5016
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 2021 (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 | |
|---|---|
| SS 2021 | SS 2016 |
Basic Information
MA5016 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
Multilinear mappings and their properties. Differentialforms. Exterior product and derivative. Derivatives and integrals of differential forms. Theorem of Stokes and connections to classical vector analysis. Physical interpretation of differential forms and application to electrodynamics.
Learning Outcome
At the end of the module, students are able to understand differential forms as an extension of the classical vector calculus to n dimensions, and express physical concepts in a oordinate-free formulation.
Preconditions
Analysis 1 [MA0001], Analysis 2 [MA0002], Analysis 3 [MA0003], Linear Algebra 1 [MA0004] , Linear Algebra 2 and Discrete Structures [MA0005]
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Learning and Teaching Methods
Lectures with mathematical proofs on the blackboard, exercise sheets with problems for preparation in homework, tutorials for discussion of solutions to exercise sheets.
Media
Tablet with projection
Literature
H. Cartan, Differentialformen, Bibliographisches Institut, Mannheim, 1985.
H. Holmann u. H. Rummler, Alternierende Differentialformen, Bibliographisches Institut, Mannheim, 1972.
I. Agricola u. T. Friedrich, Global Analysis: Differential Forms in Analysis, Geometry, and Physics, AMS Graduate Studies in Mathematics, Vol. 52, 2002.
M. do Carmo, Differential Forms and Applications, Springer Universitext, Berlin,1994.
H. Flanders, Differential Forms with Applications to the Physical Sciences, Dover Publications, New York, 1989.
S. Weintrau, Differential Forms: Theory and Practice, Academic Press, San Diego, 2014.
H. Holmann u. H. Rummler, Alternierende Differentialformen, Bibliographisches Institut, Mannheim, 1972.
I. Agricola u. T. Friedrich, Global Analysis: Differential Forms in Analysis, Geometry, and Physics, AMS Graduate Studies in Mathematics, Vol. 52, 2002.
M. do Carmo, Differential Forms and Applications, Springer Universitext, Berlin,1994.
H. Flanders, Differential Forms with Applications to the Physical Sciences, Dover Publications, New York, 1989.
S. Weintrau, Differential Forms: Theory and Practice, Academic Press, San Diego, 2014.
Module Exam
Description of exams and course work
The module examination is based on a 30-minute oral exam. Students are able to understand differential forms as an extension of the classical vector calculus to n dimensions, and express physical concepts in a oordinate-free formulation.
Exam Repetition
The exam may be repeated at the end of the semester.