Functional Analysis WS 2015/2016

 

Announcement

Students who wish to see their results from the first exam can do so next monday, Februrary 29th, from 2:00-3:00 in room 2.040.

 

Synopsis

The course covers basic functional analytic methods and their application to partial differential equations such as

• Banach spaces, Hahn-Banach Theorem, Banach-Steinhaus theorem, weak convergence
• Lebesgue- and Sobolev-spaces
• Hilbert spaces, Lax-Milgram theorem, spectral theory
• elliptic PDEs

Lecture

• Wednesday, 10-12, We10/kleiner Hörsaal
• Friday, 8-10, We10/kleiner Hörsaal

Exercises

In order to be admitted to the exam you have to achieve at least 50% of the cumulative points in the exercises.

There are  four exercise groups. 

• Monday, 12-14, N0.007 Constantin Eichenberg
• Wednesday, 16-18, N0.008 Immanuel Zachhuber
• Friday, 12-14, 1.007 Tobias Schmidt
• Friday, 12-14, Großer Hörsaal (Wegelerstraße) Qi Cheng Hua

Exercise sheets are available every Friday in the lecture and online. They are to be handed in one week later also during the Friday lecture.  Homework may be handed in by groups of at most two students.

• sheet 1
• sheet 2 (Added hint concerning the definition of bounded operators)
• sheet 3
• sheet 4
• sheet 5
• sheet 6 (With additional hint for problem 2)
• sheet 7
• sheet 8
• sheet 9
• sheet 10 (Corrected point distribution for problem 2)
• sheet 11 (Corrected definition of p in problem 3)
• sheet 12 (Hand in on Wednesday, 3.2.!)

 

 

Exams

• You have the possibility to have a look at your graded exams on Monday, April the 4th, in room 2.040 at 14.00h.

Literature

There are many books on functional analysis, for instance

• H.W. Alt, Lineare Funktionalanalysis, Springer
• H. Brezis, Functional Analysis and Partial Differential Equations, Springer
• M. Reed, B. Simon, Methods of modern mathematical physics. Volume 1: Functional Analysis, Academic Press