Mathematical Institute of the University of Bonn

RG Analysis and Partial Differential Equations

V3B1 - PDG und Funktionalanalysis, PDE and Functional Analysis (Wintersemester 2016/2017/ Winter term 2016/2017)

Instructor: Prof. Dr. Herbert Koch
Assistant: Dr. Xian Liao

Time and Place:

Wednesday, 10 (c.t.) - 12, Kleiner Hörsaal (Wegelerstr. 10)
Friday, 08 (c.t.) - 10, Kleiner Hörsaal (Wegelerstr. 10)

Office hours:

Wednesday, 12 - 1 p.m. and by appointment

Contents:

Distributions and Fourier transform, examples of Banach spaces: Lebesgue spaces and their duals, spaces of continuous functions and measures, Sobolev spaces. The structure theorems of functional analysis and applications: The theorem of Hahn- Banach, Banach-Steinhaus and the uniform boundedness principle, closed graph and open mapping theorem. Spectral theory of compact operators. The Lemma of Lax-Milgram and elliptic PDEs. Examples of bounded operators and applications to PDE.

Literature:

• Alt: Linear functional analysis / Lineare Funktionalanalysis. Springer.
• Lieb and Loss: Analysis. AMS
• Werner: Funktionalanalysis. Springer

Required and recommended background:

• Required: Good knowledge of Lebesgueintegral.
• Recommended: Basic knowledge of PDEs (harmonic functions, heat equation, Poisson problem)

Tutorials:

Time	Room	Tutor
Mo 8-10 am	SemR 0.007	Tobias Friesel
Tu 4-6 pm	SemR 0.007	Florian Schweiger
We 8-10 am	SemR 0.007	Dimitrije Cicmilovic
Fr 10-12 am	SemR 0.007	Leona Schlöder

Notes:

• Notes

Exercise Sheets:

• Exercise Sheet No. 1 (Due: 28.10.2016)
• Exercise Sheet No. 2 (Due: 04.11.2016)
• Exercise Sheet No. 3 (Due: 11.11.2016)
• Exercise Sheet No. 4 (Due: 18.11.2016)
• Exercise Sheet No. 5 (Due: 25.11.2016)
• Exercise Sheet No. 6 (Due: 02.12.2016)
• Exercise Sheet No. 7 (Due: 09.12.2016)
• Exercise Sheet No. 8 (Due: 16.12.2016)
• Exercise Sheet No. 9 (Due: 23.12.2016)
• Exercise Sheet No.10 (Due: 20.01.2017)
• Exercise Sheet No.11 (Due: 27.01.2017)

Exercises collected by Leona Schlöder

Have a try




Klausur/Written examination Termin I:

18.02.2017 09:00 - 11:00 h,
geänderter Raum/ new room: Großer Hörsaal (Wegelerstr. 10).
Einlass/Room admission: 8:45 h.
Während der Klausur sind außer Schreibmaterial, Ihrem Studenten- und amtlichen Lichtbildausweis und Nahrungsmitteln keine weiteren Gegenstände an Ihrem Platz erlaubt. Halten Sie bitte Ihren Studentenausweis sowie Ihren amtlichen Lichtbildausweis bereit.
During the examination no other objects than writing materials, student ID, identity card and food are allowed. Please make sure that you have your student ID and identity card at hand.

Klausureinsicht:

20.02.2017, 16:00 - 17:30 h, Raum 0.011



Klausur/Written examination Termin II:

29.03.2017 09:00 - 11:00 h,
Raum/ room: Großer Hörsaal (Wegelerstr. 10).
Einlass/Room admission: 8:45 h.
Während der Klausur sind außer Schreibmaterial, Ihrem Studenten- und amtlichen Lichtbildausweis und Nahrungsmitteln keine weiteren Gegenstände an Ihrem Platz erlaubt. Halten Sie bitte Ihren Studentenausweis sowie Ihren amtlichen Lichtbildausweis bereit.
During the examination no other objects than writing materials, student ID, identity card and food are allowed. Please make sure that you have your student ID and identity card at hand.

Klausureinsicht:

30.03.2017, 16:00 - 17:00 h, Raum 0.011