Coursebooks 2016-2017

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Advanced analysis I

MATH-400

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 concept of measures and probabilities, to that of Lebesgue's integral as well as to the idea of Fourier.

Content

  1. Measuring sets
  2. Integrating measurable functions
  3. Convergence theorems
  4. Fubini's theorem
  5. Normed spaces
  6. Banach spaces

Keywords

System of sets, fields, Lebesgu-Stieltjes measures, probabilities measures generated by monotn mappings, Lebesgue's integral, integrability and quasi-integrability, monotone convergence theorem, deminated convergence theorem, Fubini's therem, noremd Spaces, Banach spaces, Lp-spaces

Learning Outcomes

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

Transversal skills

Teaching methods

Ex cathedra lecture with exercises

Expected student activities

Understanding the mathematical language necessary for a deep understanding of the notions of measure and integral as well as of the notion of function spaces.

Assessment methods

Oral exam

Supervision

Office hours No
Assistants No
Forum No

Resources

Bibliography

M. Capinski, E. Kopp : Measure, Integral and probability, Springer.

Y. M. Berezansky, Z. G. Sheftel, G. F. Us: Functiona Analysis (I & II), Birkhäuser ISBN 3-7643-5344-9

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 I by Hans-Jörg Ruppen (Librairie La Fontaine)

Websites

Prerequisite for

Advanced Analysis II, probabilities, signal processing

 

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
Under construction
 
      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