MATH-404 / 5 crédits

Enseignant: Ruf Matthias Benjamin

Langue: Anglais

## Summary

We introduce locally convex vector spaces. As an example we treat the space of test functions and the space of distributions. In a second part of the course we discuss differential calculus in Banach spaces and some elements from nonlinear functional analysis.

## Keywords

Locally convex vector spaces, test functions and distributions, analysis on Banach spaces, nonlinear functional analysis

## Required courses

Analysis I-IV, Linear Algebra I-II, Metric and topological spaces, Functional analysis I

## Important concepts to start the course

Basic notions from topology, Banach spaces, differential calculus in finite dimensions

## Learning Outcomes

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

• Formulate the definitions and results of the lectures
• Apply the concepts learned in class to concrete problems
• Analyze problems related to the topics treated in the course
• Choose an appropriate method to solve a given problem
• Prove some elementary statements about the topics of the course
• Solve exercises on the topics

## Teaching methods

Weekly lectures (on blackboard) and exercise sessions with assistant

## Expected student activities

Attending the lectures and solving the exercises

## Assessment methods

Written exam

Dans le cas de l’art. 3 al. 5 du Règlement de section, l’enseignant décide de la forme de l’examen qu’il communique aux étudiants concernés.

## Supervision

 Office hours No Assistants Yes Forum Yes

No

## Bibliography

W. Rudin, Functional Analysis. McGraw-Hill, INc., 1973.

N. Bourbaki, Espaces Vectoriels Topologiques, Springer, 2007.

K. Deimling, Nonlinear Functional Analysis, Springer 1985.

## Notes/Handbook

Weekly lecture notes will be available in moodle.

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Functional analysis II
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Functional analysis II
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Functional analysis II
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 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