Spring Semester 2007

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:	Tu, Th 11:15 in Research I, 107
Grader:	Vladimir Molchanov
Email:	v.molchanov@iu-bremen.de

Time and Place:

Lectures:

Mo 9:45-11:00, We 11:15-12:30 in East Hall 3

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 March 1.
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!)

05/02/2007:	Introduction; linear transport equation
07/02/2007:	Laplace equation, fundamental solution
12/02/2007:	Poisson equation, mean value formulas
14/02/2007:	Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
19/02/2007:	Harmonic functions: analyticity
21/02/2007:	Harmonic functions: Liouville's theorem, Harnack's inequality
26/02/2007:	Dirichlet problem, Green's functions
28/02/2007:	Green's function for the half-space
05/03/2007:	Energy methods
07/03/2007:	Heat equation: fundamental solution, solution formulas
12/03/2007:	Mean value formulas for the heat equation, maximum principle
14/03/2007:	Maximum principle on unbounded domains
19/03/2007:	Regularity
21/03/2007:	Energy methods, backward uniqueness
26/03/2007:	Wave equation: D'Alembert's formula, energy methods
28/03/2007:	Midterm review
11/04/2007:	Midterm Exam
16/04/2007:	Tools from functional Analysis
18/04/2007:	Reaction-Diffusion equation (overview)
23/04/2007:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation I
25/04/2007:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation II
30/04/2007:	Special topics
02/05/2007:	Special topics
07/05/2007:	Presentation
09/05/2007:	Presentation
14/05/2007:	Presentation
16/05/2007:	Review for final exam
TBA	Final Exam

Last modified: 2007/03/22
This page: http://math.iu-bremen.de/oliver/teaching/iub/spring2007/math362/index.html
Marcel Oliver (m.oliver@iu-bremen.de)

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