Functional Analysis - Summer term 2011 (SoSe 2011)

Thomas Østergaard Sørensen

Make-up exam / Wiederholungsklausur:

Friday 21. October 2011, 16:00-18:00 (in B005 and B006). Conditions: See below.
If you wish to participate, please send an email to either Oliver Matte or Thomas Sorensen.

Result of the Make-up exam

(Wiederholungs-)Klausur-einsicht: Tue Oct 25th and Thu Oct 27, 13:15-14:00 in B408 (prof Sorensen).

Results of the (first) exam.

Time and place:

Lectures (Prof. Sørensen):
Wednesday/Friday 8:15--10:00, Room B 051. (Starts May 4th).

Exercise sessions ("Übungen") (PD Oliver Matte):
Monday 16:15--18.00, B 051. (Starts May 9th.)

Change last week: Lectures: Monday July 25th, 16:15--18.00, Wednesday July 27th, 8:15--10:00. Exercise sessions Friday July 29th, 8:15--10:00 ("Klausur-vorrechnung").

Tutorium/repetitorium sessions (Torben Krüger, Matte, Sørensen):
Tuesday 08:15--10:00, Room B 004. (Oliver Matte - Starts May 10th.)
Wednesday 10:15--12:00, Room B 040. (Thomas Sørensen - Starts May 11th.)
Thursday 08:15--10:00, Room B 040. (Torben Krüger - Starts May 12th.)
Thursday 16:15--18:00, Room B 047. (Torben Krüger - Starts May 12th.)

(For organisation and programme for the exercises, and tutorium, see the link above. To participate, you need to sign up here.)

Office hours:
Thomas Østergaard Sørensen (Room B 408): Thursday, 10:00--11:00
Oliver Matte (Room B 404): Monday, 14:00--15:00
Torben Krüger (Room B 208): Thursday, 10:00--11:00

Graders/Korrektoren: See the webpage of the Exercises (PD Matte).

General information for the course:

Functional analysis can be viewed as ``linear algebra on infinite-dimensional vector spaces'', where these spaces (often) are sets of functions. As such it is a merger of analysis and linear algebra. The concepts and results of functional analysis are important to a number of other mathematical disciplines, e.g., numerical mathematics, approximation theory, partial differential equations, and also to stochastics; not to mention that the mathematical foundations of quantum physics rely entirely on functional analysis. This course will present the standard introductory material to functional analysis (Banach and Hilbert spaces, dual spaces, Hahn-Banach Thm., Baire Thm., Open Mapping Thm., Closed Graph Thm.). We will also cover Fredholm theory for compact operators and the spectral theorem. These are powerful tools for applications to PDE's and quantum mechanics, respectively.

Students of Mathematics, Wirtschaftsmathematik, and physics; students in the International Master Programme.
("Gilt für Bachelorprüfungen Mathematik (WP4) und Wirtschaftsmathematik (P12), Masterprüfung Wirtschaftsmathematik (WP11), Diplomhauptprüfung Mathematik (RM,AM), Diplomhauptprüfung Wirtschaftsmathematik (Kernfach D)").

Introductory courses in analysis and linear algebra (Analysis I-III, Lineare Algebra I-II).

Requirement for passing the course:
The course ends with a written final exam (time: Friday, July 22nd, 15:00--17:30; more details below). The final grade is given based upon the performance on this exam. It is expected that 50% performance will be enough to pass the course, but this number may change slightly. There will be weekly exercise sheets that can be handed in for grading (in the designated box near the library on the first floor). NO LATE HOMEWORK IS ACCEPTED. (For more details, see the Exercise webpage.) To encourage the regular course work during the semester, the correct solutions to the homework will be counted as bonus points towards the final grade as follows: If one gets 40% or more of the total points on the Exercise Sheets, then the final mark at the Klausur is raised by 0.3/0.4 EXCEPT for marks below 4.0 (and, for 1.0 of course!)

Endklausur (Final (written) Exam):

Time: Friday, July 22nd, 15:00--17:30.
Place: Schellingstr. 3 (!), S 001.

Material: Complete material of all lectures up until and including Friday July 15th, and Exercise sheets up until and including Sheet 10. The solutions to Sheet 10 will be posted on July 18.

You are allowed to bring 1 (one) two-sided cheat sheet (Spickzettel): a piece of A4-paper on which you have written (on both sides) whatever you think might be useful for the Klausur/exam. You may not bring anything else (apart from pens/pencils), i.e., no books, notes from class, homework, solutions to homework etc. Examination booklet and extra paper will be provided. Put your name on every sheet you wish to hand in, and write readable.

There will be more problems than you need to solve to get the maximal point (100%), so you will have some freedom to choose, but you can attempt all of them and collect partial credits.

The final grade is determined by the final exam plus the bonus points from homework, see the precise rules above.

There will be no make-up exam (keine Nachholklausur). If necessary, there will be another exam (Wiederholungsklausur) offered around mid October for those who failed the first one (precise date is to be fixed). This will be a new exam, i.e. all grades from the first exam will be reported to the Prüfungsamt. According to the Exam Rules (Prüfungsordnung), the second exam cannot be used the improve the grade on the first one (III. Paragraph 11 (7) of the Prüfungsordnung).

The exam in October will be similar to the one on July 22nd, but bonus points from the homework will not be counted; the grade will be determined solely by the result on that exam. This restriction rule will not apply to those who missed the exam on July 22nd for a properly documented health reason (see III. Paragraph 11. (5) Satz 4--7 of the Prüfungsordnung).

Exercise Sheets:
Will be posted on the web every Monday by 12.00 noon on the exercise homepage. Solutions are due the following Monday at 12:00 noon in the designated box. First sheet is posted on May 9th. For more details, see the exercise homepage.

The lectures, the webpage and our main literature are in English. The purpose is double: to strengthen the English knowledge of the German students and to make the lectures accessible to non-German Master students. The exercise sessions are also held in English, by default. However, Herr Krüger, Dr. Matte, and Pr. Sørensen are ready to switch to German in private discussions. If you feel that your English is not strong enough to ask questions, please do it in German. The questions on the Exercise sheets and on the Klausur will be in English, but the solutions can be turned in either in German or in English.

There will be no comprehensive Skript (Lecture Notes), since we mainly follow excellent textbooks. The course will not follow a particular textbook. The list below provides a short selection of English and German textbooks on the subject (of which there are many!). Note that most of them cover the material of a two-semester course. The brief contents of the lectures will keep you updated, here you will find the more precise references.

Contents (preliminary):


Last update: October 11th, 2011 by Thomas Østergaard Sørensen.