Analysis IV

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. 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

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

Moodle Link

• https://go.epfl.ch/MATH-205

Prerequisite for

Master cycle of mathematics