Workgroup Applied Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.029

Englerstrasse 2
76131 Karlsruhe
Germany

Dr. Kaori Nagato-Plum
kaori.nagatou@kit.edu

Office hours:
Mon - Fri 10:00 -- 12:00

Tel.: +49 721 608 42056

Fax.: +49 721 608 46214

# Functional Analysis (Winter Semester 2012/13)

 Lecturer: Prof. Dr. Dirk Hundertmark Lecture (0104800), Problem class (0104900) 4+2

The lectures on Functional Analysis will cover the fundamental concepts of metric spaces, Banach spaces, the Hahn-Banach separation theorem, open mapping theorem, uniform boundedness principle, the closed range theorem, duality and compactness. Our approach will be less focused on discussing the most abstract concept in detail, but we will discuss the extremely powerful and versatile tools Functional Analysis gives for Applied Mathematics, in particular, a modern approach to Partial Differential Equations.

 Lecture: Problem class: Tuesday 9:45-11:15 Nusselt-Hörsaal Begin: 16.10.2012 Thursday 11:30-13:00 Hertz-Hörsaal Friday 14:00-15:30 Eiermann Begin: 19.10.2012
 Lecturer Prof. Dr. Dirk Hundertmark Office hours: Room 2.028 Kollegiengebäude Mathematik (20.30) Email: dirk.hundertmark@kit.edu Silvana Avramska-Lukarska Office hours: Tue, 11-12h and by appointment Room 2.026 Kollegiengebäude Mathematik (20.30) Email: silvana.avramska-lukarska@kit.edu

The lecture covers fundamental aspects of linear functional analysis.

Topics:

• metric spaces, Banach spaces
• main principles of functional analysis (Hahn-Banach theorem, principle of uniform boundedness, closed graph theorem)
• weak convergence, Banach-Alaoglu theorem
• Hilbert spaces

# Lecture Notes

 Lecture Notes

# IMPORTANT

On Friday, Feb. 1, 2013, the exercise class will take place at the usual time BUT in room Kleiner HS B, Building 30.22!

# Exercise Sheets

 Exercise Sheet 1 Solutions 1 Exercise Sheet 2 Solutions 2 Exercise Sheet 3 Solutions 3 Exercise Sheet 4 Solutions 4 Exercise Sheet 5 Solutions 5 Exercise Sheet 6 Solutions 6 Exercise Sheet 7 Solutions 7 Exercise Sheet 8 Solutions 8 Exercise Sheet 9 Solutions 9 Exercise Sheet 10 Solutions 10 Exercise Sheet 11 Solutions 11 Exercise Sheet 12 Solutions 12 Exercise Sheet 13 Solutions 13 Exercise Sheet 14 Solutions 14

# Bonus Points

During the semester 3 bonus points for the exam can be obtained. For this one needs to achieve 50% of the points from Exercise Sheets 5 - 14.

# Examination

The examination will take place on Wednesday, March 20, 2013, at 14:00 - 16:00, in Tulla HS (Building 11.40).

Please register for the exam until Monday, March 18, 2013, via the QISPOS/Studierendenportal.

During the examination the use of two one-sided handwritten DIN A4 pages (or equivalenty, one double-sided handwritten DIN A4 page) is allowed.

The written examination will be in English!

The post-exam review ("Klausureinsicht") will take place on Wednesday, April 17, 2013, at 15:45-16:45 in room 1C-01 (Building 05.20).

# References

H. Brezis: Functional Analysis, Sobolev spaces and Partial Differential Equations, Springer 2011
D. Werner: Funktionalanalysis, Springer 2011