Operator Theory
Module MA5012
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 2011/2 (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 | |
|---|---|
| WS 2011/2 | SS 2011 |
Basic Information
MA5012 is a semester module in English language at Master’s level which is offered once.
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
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 270 h | 90 h | 9 CP |
Content, Learning Outcome and Preconditions
Content
Spectrum of operators, spectral theory of normal operators, functional calculus for various classes of operators. Applications for integral operators and differential operators.
Learning Outcome
At the end of module, students are able to analyze and synthesize various operators showing up when dealing with partial differential equations and inverse problems.
Preconditions
MA3001 Functional Analysis
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 4 | Operator Theory | Warzel, S. Young, A. |
Tue, 14:15–15:45, MI 03.08.011 Thu, 12:15–13:45, MI 03.08.011 |
|
| UE | 2 | Operator Theory (Exercise Session) | Warzel, S. Young, A. |
Wed, 16:15–17:45, MI 02.08.020 and singular or moved dates |
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 encourage the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding the lectures, practice sessions will be offered, in which students will be working through exercises provided in class. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. As the term progresses, students will be working increasingly independently or in small groups towards their course project.
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 encourage the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding the lectures, practice sessions will be offered, in which students will be working through exercises provided in class. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. As the term progresses, students will be working increasingly independently or in small groups towards their course project.
Media
blackboard
Literature
Dunford, Schwartz: Linear Operators I-III, Wiley-Interscience 1988.
Weidmann: Lineare Operatoren im Hilbertraum, Teubner 1986.
Werner: Funktionalanalysis, Springer 2007.
Weidmann: Lineare Operatoren im Hilbertraum, Teubner 1986.
Werner: Funktionalanalysis, Springer 2007.
Module Exam
Description of exams and course work
The module examination is based on a written exam (90 minutes). Students have to understand the fundamental notions, techniques and methods in spectral theory and be able to apply them to simple examples.
Exam Repetition
The exam may be repeated at the end of the semester.