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