MATH-205 / 7 credits
Teacher: Colombo Maria
Learn the basis of Lebesgue integration and Fourier analysis
- Measurable sets and functions
- Lebesgue integral
- Monotone and dominated convergence theorems
- L^p spaces
- Fourier series
- Introduction to Fourier transform
- Applications to partial differential equations
Analysis I, II, III
- 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
Lectures and assisted/discussed exercises
Written exam. The evaluated exercise each week will provide a bonus of up to 1.2.
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
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