Fall Semester 2008

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@jacobs-university.de
Phone:	200-3212
Office hours:	Mo, Fr 11:15 in Research I, 107
Grader:	Mahmut Çalik
Email:	m.calik@jacobs-university.de

Time and Place:

Lectures:

We, Fr 9:45 in East Hall 3

Recommended 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: 10%

Midterm Exam: 30%

Final Exam: 40%
Each participant will give an approximately half-hour presentation toward the end of the semester. A topic should be chosen until October 1.
Each of the individual scores will be converted to Jacobs grade points before the overall weighted grade point average is computed.

Class Schedule (subject to change!)

03/09/2008:	Introduction; linear transport equation
05/09/2008:	Laplace equation, fundamental solution
10/09/2008:	Poisson equation, mean value formulas
12/09/2008:	Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
17/09/2008:	Harmonic functions: analyticity
19/09/2008:	Harmonic functions: Liouville's theorem, Harnack's inequality
24/09/2008:	Dirichlet problem, Green's functions
26/09/2008:	Green's function for the half-space; energy methods
01/10/2008:	Heat equation: fundamental solution, solution formulas
08/10/2008:	Mean value formulas for the heat equation, maximum principle
10/10/2008:	Maximum principle on unbounded domains
15/10/2008:	Regularity
17/10/2008:	Energy methods, backward uniqueness
22/10/2008:	Wave equation: D'Alembert's formula, energy methods
24/10/2008:	Midterm review
29/10/2008:	Midterm Exam
31/10/2008:	Midterm return and discussion
05/11/2008:	Tools from Functional Analysis
07/11/2008:	Reaction-Diffusion equations (overview)
12/11/2008:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation I
14/11/2008:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation II
19/11/2008:	Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation III
21/11/2008:	Introduction to scalar conservation laws I
26/11/2008:	Introduction to scalar conservation laws II
28/11/2008:	Presentation
03/12/2008:	Presentation
05/12/2008:	Review for final exam
11/12/2008:	Final Exam, 13:00-15:00 in East Hall 4

Last modified: 2008/11/27
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2008/math362/index.html
Marcel Oliver (m.oliver@jacobs-university.de)

Homework:	20%
Presentation:	10%
Midterm Exam:	30%
Final Exam:	40%