250099 VO Selected topics in Fourieranalysis (2015W)
Labels
Details
Language: German
Examination dates
- Friday 29.01.2016
- Friday 11.03.2016
- Friday 11.03.2016
- Thursday 30.06.2016
- Thursday 22.09.2016
- Wednesday 05.04.2017
Lecturers
Classes (iCal) - next class is marked with N
- Monday 05.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 07.10. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 12.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 14.10. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 19.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 21.10. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 28.10. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 04.11. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 09.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 11.11. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 16.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 18.11. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 23.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 25.11. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 30.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 02.12. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 07.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 09.12. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 14.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 16.12. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 11.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 13.01. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 18.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 20.01. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 25.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 27.01. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Series expansions. Definition of Fourier series. Related expansions. Bessel's inequality. Pointwise and uniform convergence of Fourier series. Periodic solutions of differential equations. The vibrating string. Convolution equations. Mean square convergence. Schwartz space S. Fourier transform in S. Inverse Fourier transform. Parseval's formula. Solutions of differential equations with constant coefficients.
Assessment and permitted materials
Written exam (2 hours).
Minimum requirements and assessment criteria
The purpose is to introduce the notions of Fourier series and Fourier transform and to study their basic properties. The main part of the course will be devoted to the one dimensional case in order to simplify the definitions and proofs. Many multidimensional results are obtained in the same manner, and those results will also be discussed (briefly). Fourier analysis techniques are important in various fields, in particular, in mathematical physics. It will be explained how one can solve some differential equations and study the properties of their solutions using these techniques.
Examination topics
Pre-requisistes are calculus, linear algebra and a basic course
on differential equations. In the beginning some key results
from integration theory and functional analysis
will be discussed.
on differential equations. In the beginning some key results
from integration theory and functional analysis
will be discussed.
Reading list
A. Constantin, Fourier analysis with applications, Cambridge University Press, 2015.
(in print)
(in print)
Association in the course directory
MANV
Last modified: Mo 07.09.2020 15:40