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 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	WS 2020/1	WS 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 workload	Contact hours	Credits (ECTS)
270 h	120 h	9 CP

Content, Learning Outcome and Preconditions

Content

Sigma algebra, Borel sigma algebra, Lebesgue measure and integral: Fubini, transformation formula, convergence theorems, push-forward 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.

Preconditions

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

WS 2022/3 WS 2021/2 WS 2020/1

Type	SWS	Title	Lecturer(s)	Dates	Links
VO	4	Analysis 3 [MA0003]	Johann, A. Zimmer, J.	singular or moved dates	eLearning
UE	2	Analysis 3 (Exercise Session) [MA0003]	Johann, A. Zimmer, J.	dates in groups
UE	2	Analysis 3 (Central Exercise) [MA0003]	Johann, A. Zimmer, J.	singular or moved dates	eLearning

Learning and Teaching Methods

lecture, exercise module

Media

blackboard

Literature

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.
W. Rudin, Real and complex analysis, 3rd edition, McGraw-Hill 1987

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.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
Time	Location	Info	Registration
Analysis 3
Mon, 2023-02-27, 8:00 till 9:30	Hörsaal 1801 2501		till 2023-01-15 (cancelation of registration till 2023-02-20)
Thu, 2023-04-13, 11:00 till 12:30	101 102		till 2023-03-27 (cancelation of registration till 2023-04-06)