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
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 2012||WS 2011/2|
MA4064 is a semester module in English language at Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
|Total workload||Contact hours||Credits (ECTS)|
|150 h||45 h||5 CP|
Content, Learning Outcome and Preconditions
2. Fourier transform. Definition on L^1(R^n) and basic properties (inversion formula; behaviour under multiplication, convolution, differentiation). Definition on L^2 and Plancherel's formula. The space of tempered distributions and Fourier calculus on distributions. Periodic arrays of delta functions and Poisson summation. Selected applications of the Fourier transform, e.g. solution of partial differential equations, Heisenberg uncertainty, X-ray crystallography, Shannon sampling and digitalization of acoustic signals, construction of wavelets.
Courses, Learning and Teaching Methods and Literature
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.
R. Strichartz, A guide to distribution theory and the Fourier transform (CRC Press, 1994).
M. Reed, B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness (Academic Press, 1975).