de | en

# Differential Forms

## Module MA5016

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 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 2021SS 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
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

VO 2 Differential Forms Massopust, P. eLearning
UE 2 Differential Forms (Exercise Session) Massopust, P. Thu, 14:00–16:00, virtuell

#### 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.

### 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.

Top of page