Analysis 2
Module MA1002
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 2014/5
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 | |||
|---|---|---|---|
| WS 2020/1 | SS 2020 | SS 2015 | WS 2014/5 |
Basic Information
MA1002 is a semester module in German language at Bachelor’s level which is offered in summer 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) |
|---|---|---|
| 300 h | 105 h | 10 CP |
Content, Learning Outcome and Preconditions
Content
Power series (in particular disk of convergence and complex exponential function).
Fourier series.
Explicit solutions of simple ordinary differential equations.
Analysis in Rn (differentiation of vector fields and Taylor expansion).
Norms and completeness. Equivalence of norms in Rn.
Open, closed and compact sets in Rn, Bolzano Weierstrass theorem
Banach fixed point theorem for closed subsets of complete normed spaces.
Implicit functions.
Maximization and minimization problems, Lagrange multipliers.
Explicit evaluation of elementary multiple integrals.
Fourier series.
Explicit solutions of simple ordinary differential equations.
Analysis in Rn (differentiation of vector fields and Taylor expansion).
Norms and completeness. Equivalence of norms in Rn.
Open, closed and compact sets in Rn, Bolzano Weierstrass theorem
Banach fixed point theorem for closed subsets of complete normed spaces.
Implicit functions.
Maximization and minimization problems, Lagrange multipliers.
Explicit evaluation of elementary multiple integrals.
Learning Outcome
Following the successful completion of the module, students understand the theoretical concepts of real multidimensional analysis and can handled them safely in example situations.
Preconditions
MA1001 Analysis 1, MA1101 Linear Algebra und Discrete Structures 1
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 5 | Analysis 2 [MA0002] | Kruse, H. Zimmer, J. |
Mon, 10:15–11:45, virtuell Tue, 10:15–11:45, virtuell Fri, 08:30–09:15, virtuell |
eLearning |
| UE | 1 | Analysis 2 (Questtion Time) [MA0002] | Zimmer, J. |
Fri, 09:15–10:00, virtuell |
|
| UE | 2 | Analysis 2 (Exercise Session) [MA0002] | Kruse, H. Zimmer, J. | dates in groups | |
| UE | 2 | Analysis 2 (Central Exercise Session) [MA0002] | Kruse, H. Zimmer, J. |
Wed, 11:30–13:00, virtuell |
Learning and Teaching Methods
lecture, tutorial, supplement lecture
Media
blackboard, assignments
Literature
K. Königsberger, Analysis 1, 6. Auflage, Springer 2003.
W. Rudin, Principles of Mathematical Analysis, 2nd ed, McGraw Hill, 1964.
W. Rudin, Principles of Mathematical Analysis, 2nd ed, McGraw Hill, 1964.
Module Exam
Description of exams and course work
The module examination is based on a written exam (90 minutes). Students have to give a compressed display of theoretical basics of real multidimensional analysis. They are able to discuss connections with example problems under time pressure.
Exam Repetition
The exam may be repeated at the end of the semester.