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
Module version of WS 2011/2
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.
MA2004 is a semester module
in German language
at Bachelor’s level
which is offered in winter semester.
This module description is valid to SS 2021.
Surfaces and manifolds in Rn. Line and surface integrals. The classical Gauss divergence theorem and Stokes' theorem and generalizations.
Having successfully completed this module, the student is able to deal with subsets of n dimensional space which are described by nonlinear functions, and with the corresponding linear approximations as well as with differential and integral formulas on those objects.
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2
Courses and Schedule
Learning and Teaching Methods
The module is offered as lectures with accompanying 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 animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.
K.Jänich, Vektoranalysis, Springer, 2005. English translation: Vector analysis. Springer, 2001.
J.R. Munkres, Analysis on manifolds, Perseus 1991.
M. Spivak, Calculus on Manifolds, Perseus 1965.
Description of exams and course work
The module examination is based on a written exam (60 minutes). Students have to deal with subspaces of the n-dimensional space described by nonlinear functions and with linear approximations. They have to apply differential and integral calculus to these subspaces adequately.
The exam may be repeated at the end of the semester.