Functional Analysis (Winter Semester 2012/13)
- Lecturer: Prof. Dr. Dirk Hundertmark
- Classes: Lecture (0104800), Problem class (0104900)
- Weekly hours: 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.
| Schedule | |||
|---|---|---|---|
| Lecture: | Tuesday 9:45-11:15 | Nusselt-Hörsaal | Begin: 16.10.2012 |
| Thursday 11:30-13:00 | Hertz-Hörsaal | ||
| Problem class: | Friday 14:00-15:30 | Eiermann | Begin: 19.10.2012 |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Dr. Dirk Hundertmark | |
| Office hours: | ||
| Room 2.028 Kollegiengebäude Mathematik (20.30) | ||
| Email: dirk.hundertmark@kit.edu | Problem classes | 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
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
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