5 credits
30.0 h + 22.5 h
Q2
Teacher(s)
Willem Michel;
Language
French
Prerequisites
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
Metric spaces, Lebesgue integral, normed spaces, Hilbert spaces.
Aims
At the end of this learning unit, the student is able to : | |
| 1 | AA 1.1, 1.2, 1.3, 3.1, 6.1. |
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
- Metric spaces, continuity, convergence.
- Cauchy integral, Lebesgue integral, multiple integrals, change of variables.
- Normed spaces, continuous linear mappings, Hilbert space, elementary spectral theorem
Teaching methods
Lectures with dialoguee, exercises. The main points are critical understanding of the theory and active problem solving.
Evaluation methods
Written examination : theory, exercises and partly original problems.
Other information
Online resources
Bibliography
Livre de référence : Michel Willem, « Functional Analysis. Fundamentals and Applications », Birkhauser, 2013. Disponible en ligne et en librairie.
Faculty or entity
MAP