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Analysis 3

Module MA0003

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 WS 2019/20

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 2021WS 2020/1WS 2019/20

Basic Information

MA0003 is a semester module in German language at Bachelor’s level which is offered in winter semester.

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

  • Further Modules from Other Disciplines
Total workloadContact hoursCredits (ECTS)
270 h 120 h 9 CP

Content, Learning Outcome and Preconditions


Sigma algebra, Borel sigma algebra, Lebesgue measure and integral: Fubini, transformation formula, convergence theorems, push-fowarward measure, density with respect to Lebesgue measure, Lebesgue spaces: inequalities, completeness, Hilbert space, manifold in R^n, surface integral, theorems of Gauss and Stokes.

Learning Outcome

After successfully attending this course, students are familiar with the basic concepts and results of Lebesgue integration theory. They also know how to adequately apply differential and integral calculus on subspaces of R^n described by nonlinear functions.


MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 und Discrete Structures

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Analysis 3 [MA0003] Kreiner, C. Warzel, S. Thu, 16:15–17:45, virtuell
Mon, 14:00–16:00, virtuell
and singular or moved dates
UE 2 Analysis 3 (Exercise Session) [MA0003] Kreiner, C. Warzel, S. dates in groups
UE 2 Analysis 3 (Central Exercise) [MA0003] Kreiner, C. Warzel, S. Tue, 14:00–16:00, virtuell
and singular or moved dates

Learning and Teaching Methods

lecture, exercise module




M. Brokate, G. Kersting: Maß und Integral, Birkhäuser, 2010.
D. Werner: Kap IV aus: Einführung in die höhere Analysis, Springer 2006.
K. Jänich: Vektoranalysis, Springer 2005.
J.R. Munkres: Analysis on Manifolds, Perseus 1991.

Module Exam

Description of exams and course work

The module examination is based on a written exam (90 minutes). Students are tested whether they know and can apply the basic concepts of Lebesgue’s integration theory. They are also asked to apply differential and integral calculus on subspaces of Rn described by nonlinear functions.

Exam Repetition

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

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