MATH-404 / 5 credits

Teacher: Ruf Matthias Benjamin

Language: English


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.

Content

Keywords

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

Learning Prerequisites

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

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

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

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

K. Deimling, Nonlinear Functional Analysis, Springer 1985.

 

Ressources en bibliothèque

Notes/Handbook

Lecture notes will be available in moodle.

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Functional analysis II
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Functional analysis II
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Functional analysis II
  • Lecture: 2 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