Analysis IV

MATH-205 / 7 credits

Teacher: Colombo Maria

Language: English

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

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

Moodle Link

Prerequisite for

Master cycle of mathematics

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Lecture: 3 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

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