MATH-205 / 7 crédits

Enseignant: Colombo Maria

Langue: Anglais


Summary

Learn the basis of Lebesgue integration and Fourier analysis

Content

Learning Prerequisites

Required courses

Analysis I, II, III

Learning Outcomes

  • Describe the fundamental concepts on the Lebesgue measure, the Lebesgue integration and the Fourier series/transform
  • Define the objects and prove their properties
  • Solve exercises and identify meaningful examples
  • Use the Fourier series/transform to solve linear PDEs

Teaching methods

Lectures and assisted/discussed exercises

Assessment methods

Written exam. The evaluated exercise each week will provide a bonus of up to 1.2.

Supervision

Assistants Yes

Resources

Bibliography

T. Tao: "Analysis II"
B. Dacorogna: Polycopié

 

E. Stein: "Real analysis: measure theory, integration, and Hilbert spaces"
E. Stein: "Fourier analysis: an introduction"

S.D. Chatterji: "Cours d'analyse 1 et 3" PPUR
S.D. Chatterji: "Equations différentielles ordinaires et aux dérivées partielles"

Ressources en bibliothèque

Prerequisite for

Master cycle of mathematics

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Ecrit (session d'été)
  • Matière examinée: Analysis IV
  • Cours: 3 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
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