Coursebooks 2016-2017

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Advanced analysis II

MATH-401

Lecturer(s) :

Ruppen Hans-Jörg

Language:

English

Remarque

Advanced Analysis I and Advanced Analysis II must be taken together as a whole

Summary

Getting access to the use of Banach spaces, Hilbert spaces, Fourier series, Fourier tansforms and distributions.

Content


  1. Inner product spaces and Hilbert spaces
  2. L2 spaces
  3. Orthonormal sets in Hilbert spaces: Fourier coefficients, Bessel inequality and equality
  4. Periodic signals and Fourier series
  5. Fourier Transform in L1 and in L2
  6. Distrribution spaces
  7. Tempered distributions and Fourier transform

Keywords

inner product spaces, Hilbert spaces, Lp spaces, orthonoral sets, Fourier coefficients, Fourier transform, distributions, tempered distributions, peridoic signals, Dirac comb, sampling of a signal

Learning Prerequisites

Recommended courses

Advanced Analysis I

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Ex cathedra lecture and exercises in the classroom

Expected student activities

Understanding the mathematical language necessary for a deep understanding of signals and their transforms, of the Lebesgue spaces and the distribution spaces

Assessment methods

Oral exam

Resources

Bibliography

C. Gasquet, P. Witomski: Fourier Analysis and Applications, Springer, ISBN 0-387-98485-2

W. Kammler: A First Course in Fourier AnalysisDavid, Online ISBN: 9780511619700 Hardback ISBN: 9780521883405 Paperback ISBN: 9780521709798

 

Ressources en bibliothèque
Notes/Handbook

Lecture notes: Advanced Analysis II by Hans-Jörg Ruppen (Librairie La Fontaine)

Websites

Prerequisite for

Diploma

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14   BS260 
14-15    
15-16   BS260 
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German