Lectures and Seminars for Graduate and Undergraduate Students
Summer Semester 2013

The International Max-Planck Research School for Geometric Analysis, Gravitation and String Theory is a joint project of the Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Freie Universität Berlin (Institute for Mathematics) and Universität Potsdam.
The IMPRS aims to promote research in mathematical physics in an area related in the widest sense to Einstein's theory of general relativity, ranging from pure mathematics (differential geometry and the theory of partial differential equations) to the physics of black holes, gravitational waves and cosmological applications of Einstein's theory and all the way to the most recent efforts to reconcile Einstein's theory with quantum mechanics in the framework of superstring theory and M theory.
Our following seminars are recommended for post-graduates of the IMPRS:
- - Forschungsseminar Geometrische Analysis.
- - Oberseminar Analysis, Geometrie und Physik.
- - Differentialgeometrie und Analysis

V- 19040 Differentialgleichungen I (Theodora Bourni)

Inhalt:

• Basic Linear Partial Differential Equations; Laplace's equation, Heat equation, Wave equation.
• Sobolev spaces; Weak derivatives, Sobolev and Poincare Inequalities.
• Theory for Linear Partial Differential Equations; Existence of weak solutions and regularity.
• Linear Evolution Equations; second order parabolic equations.

Vorlesung:
Dienstag 10 - 14 Uhr - Arnimallee 14 HS B (0.1.01)

Übungsblätter
Blatt 1, Abgabe am 23.04.13
Blatt 2, Abgabe am 30.04.13
Blatt 3, Abgabe am 07.05.13
Blatt 4, Abgabe am 14.05.13 / English version
Blatt 5, Abgabe am 21.05.13 / English version
Blatt 6, Abgabe am 28.05.13 / English version
Blatt 7, Abgabe am 04.06.13 / English version
Blatt 8, Abgabe am 11.06.13 / English version
Blatt 9, Abgabe am 18.06.13 / English version
Blatt 10, Abgabe am 25.06.13 / English version

Tutorien
Donnerstag 10 - 12 Uhr - Arnimallee 6 SR 032
Freitag 12 - 14 Uhr - Arnimallee 6 SR 032

Klausur
Dienstag 9. Juli 2013, 10:15 - 11:45 - Arnimallee 14 HS B (0.1.01) (lecture room)
Klausureinsicht: Freitag 12. Juli 2013, 10:30 - 12:30 - Arnimallee 3 HH, room 132

Nachklausur
Dienstag 15. Oktober 2013, 12:00 - 14:00 Uhr, Arnimallee 6, SR 032 - Ergebnisse
Klausureinsicht: Freitag 18. Oktober 2013, 14:00 - 16:00 - Arnimallee 3 HH, room 132

Literatur:
"Partial Differential Equations" by Lawrence C. Evans

Für die erfolgreiche Teilnahme an dieser Vorlesung müssen Sie folgende Leistungen erbringen:

1. Successful participation in the exam.
2. Active and regular participation in the tutorials. This means
1. Treatment and submission of the exercise sheets and achieving at least 50% of the total marks.
   Please, get together in exercise groups of 2-3 people and submit the sheets groupwise. You are expected to have worked on any solution that is submitted by your exercise group.
2. Presentation of at least one of your group's (correct) solutions of in front of the class.

Sommersemester 2004
Wintersemester 2004-2005
Sommersemester 2005
Wintersemester 2005-2006
Sommersemester 2006
Wintersemester 2006/2007
Sommersemester 2007
Wintersemester 2007/2008
Sommersemester 2008
Wintersemester 2008/2009
Sommersemester 2009
Wintersemester 2009/2010
Sommersemester 2010
Wintersemester 2010/2011
Sommersemester 2011
Wintersemester 2011/2012
Sommersemester 2012
Wintersemester 2012/2013