MATH-205 / 7 crédits

Enseignant: Colombo Maria

Langue: Anglais

## Summary

Learn the basis of Lebesgue integration and Fourier analysis

## 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. A midterm will be organized and the final grade will be assigned according to a formula like
Final grade = \max { Final grade, 0.4 * Midterm grade + 0.6 * Final grade }

## Supervision

 Assistants Yes

## 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"

## 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

 Lu Ma Me Je Ve 8-9 9-10 10-11 CE5 11-12 CE5 12-13 13-14 CM1 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Mercredi, 13h - 15h: Cours CM1

Jeudi, 10h - 11h: Cours CE5

Jeudi, 11h - 13h: Exercice, TP CE5

## Cours connexes

Résultats de graphsearch.epfl.ch.