Functional Analysis
Module MA3001
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 2020
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 | SS 2020 | SS 2019 | WS 2011/2 | SS 2011 |
Basic Information
MA3001 is a semester module in English language at Master’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
- Catalogue of non-physics elective courses
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 270 h | 90 h | 9 CP |
Content, Learning Outcome and Preconditions
Content
- Banach and Hilbert spaces;
- Bounded linear operators, open mapping theorem;
- Spectral theory for compact selfadjoint operators;
- Duality, Hahn-Banach theorems;
- Weak and weak* convergence;
- Brief introduction to unbounded operators
- Bounded linear operators, open mapping theorem;
- Spectral theory for compact selfadjoint operators;
- Duality, Hahn-Banach theorems;
- Weak and weak* convergence;
- Brief introduction to unbounded operators
Learning Outcome
After successful completion of the module students are able to understand and apply basic theoretical techniques to analyze linear functionals and operators on Banach and Hilbert spaces. In particular, they can analyze spectra of compact selfadjoint operators, understand the notion of duality and can apply concepts of weak and weak-star convergence in Banach spaces.
Preconditions
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Lineare Algebra and Discrete Structures 2
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 and Discrete Structures
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 and Discrete Structures
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
WS 2022/3
WS 2021/2
WS 2020/1
WS 2019/20
WS 2018/9
WS 2017/8
WS 2016/7
WS 2015/6
WS 2014/5
WS 2013/4
WS 2012/3
WS 2011/2
WS 2010/1
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 4 | Functional Analysis | Bornemann, F. Ludwig, C. |
Tue, 14:00–16:00, PH HS2 Thu, 10:15–11:45, Interims II 004 |
eLearning |
| UE | 2 | Exercises for Functional Analysis | Bornemann, F. Ludwig, C. | dates in groups |
eLearning |
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 motivate 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.
Media
blackboard
Literature
·Peter D. Lax: Functional Analysis (Wiley, 2002)
·Gert K. Pedersen: Analysis Now (Springer, 1989
·John B. Conway: A Course in Functional Analysis (Springer, 1990)
·W. Rudin, Functional Analysis (McGraw Hill, 1991)
·M. Reed/B. Simon, Functional Analysis (Academic Press 1972)
·Dirk Werner: Funktionalanalysis (Springer, 1995)
·Gert K. Pedersen: Analysis Now (Springer, 1989
·John B. Conway: A Course in Functional Analysis (Springer, 1990)
·W. Rudin, Functional Analysis (McGraw Hill, 1991)
·M. Reed/B. Simon, Functional Analysis (Academic Press 1972)
·Dirk Werner: Funktionalanalysis (Springer, 1995)
Module Exam
Description of exams and course work
The module examination is based on a written exam (90 minutes). Students have to know theoretical basics and methods to analyze linear functionals and operators in Banach and Hilbert spaces. They can give solutions to application problems in limited time.
Exam Repetition
The exam may be repeated at the end of the semester.