Analysis IV - Lebesgue measure, Fourier analysis

Summary

Learn the basis of Lebesgue integration and Fourier analysis

Content

Learning Prerequisites

Required courses

Analysis I, II, III

Learning Outcomes

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

• 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

Resources

Bibliography

Polycopié of the course

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

• Analysis II / Tao
• Polycopié / Dacorogna
• Real analysis / Stein
• Fourier analysis / Stein
• Cours d'Analyse (volume 1) / Chatterji
• Equations différentielles ordinaires et aux dérivées partielles / Chatterji

Moodle Link

• https://go.epfl.ch/MATH-205

Prerequisite for

Master cycle of mathematics