Fall Semester 2004

Partial Differential Equations

Syllabus

Quick Links:

Class mailing list for announcements and discussion
Homework sheets
Class handouts and exams
Solutions to selected homework and exams

Summary:

This class is an introduction to the theory of partial differential equations. The main topics are: classification of PDEs, linear prototypes (transport equation, Poisson equation, heat equation, wave equation); functional setting, function spaces, variational methods, weak and strong solutions; examples of nonlinear parabolic PDEs, introduction to conservation laws; exact solution techniques, transform methods, power series solutions, asymptotics.

Contact Information:

Instructor:	Marcel Oliver
Email:	m.oliver@iu-bremen.de
Phone:	200-3212
Office hours:	M 15:00, W 11:00 in Research I, 107
Grader:	Shaowu Tang
Email:	s.tang@iu-bremen.de

Time and Place:

Lectures:

Tu 9:45-11:00, Th 8:15--9:30 in East Hall 8

Reommended Textbook:

L.C. Evans: Partial Differential Equations

Grading:

The final grade will be computed as a grade point average with the following weights:

Homework: 20%

Presentation: 20%

Midterm Exam: 20%

Final Exam: 40%
Each participant will give an approximately half-hour presentation toward the end of the semester. A topic should be chosen until September 21.
Each of the individual scores will be converted to IUB grade points before the overall weighted grade point average is computed.

Class Schedule (subject to change!)

31/08/2004:	No class
02/09/2004:	Introduction; linear transport equation
07/09/2004:	Laplace equation, fundamental solution
09/09/2004:	Poisson equation, mean value formulas
14/09/2004:	Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
16/09/2004:	Harmonic functions: analyticity
21/09/2004:	Harmonic functions: Liouville's theorem, Harnack's inequality
23/09/2004:	Dirichlet problem, Green's functions
28/09/2004:	Green's function for the half-space; energy methods
30/09/2004:	Heat equation: fundamental solution, solution formulas
05/10/2004:	Mean value formulas for the heat equation, maximum principle
07/10/2004:	Regularity
12/10/2004:	Energy methods, backward uniqueness
14/10/2004:	Wave equation: D'Alembert's formula, energy methods
19/10/2004:	Tools from functional Analysis I
21/10/2004:	Tools from functional Analysis II
26/10/2004:	Midterm review
28/10/2004:	Midterm Exam
02/11/2004:	Reaction-Diffusion equation (overview)
04/11/2004:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation I
09/11/2004:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation II
11/11/2004:	Special topics
16/11/2004:	Special topics
18/11/2004:	Special topics
23/11/2004:	Presentation
25/11/2004:	Presentation
30/11/2004:	Presentation
02/12/2004:	Review for final exam
09/12/2004:	Final Exam, 11:00-13:00 in the Research II Lecture Hall

Last modified: 2004/09/29
This page: http://math.iu-bremen.de/oliver/teaching/iub/fall2004/pde/pde.html
Marcel Oliver (m.oliver@iu-bremen.de)

Homework:	20%
Presentation:	20%
Midterm Exam:	20%
Final Exam:	40%