Spring Semester 2011

Introduction to 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:	Tu, Th 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 April 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!)

01/02/2011:	Introduction; linear transport equation
03/02/2011:	Laplace equation, fundamental solution
08/02/2011:	Poisson equation, mean value formulas
10/02/2011:	Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
15/02/2011:	Harmonic functions: analyticity
17/02/2011:	Harmonic functions: Liouville's theorem, Harnack's inequality
22/02/2011:	Dirichlet problem, Green's functions
24/02/2011:	Green's function for the half-space; energy methods
01/03/2011:	Heat equation: fundamental solution, solution formulas
03/03/2011:	Mean value formulas for the heat equation, maximum principle
08/03/2011:	Maximum principle on unbounded domains
10/03/2011:	Regularity
15/03/2011:	Energy methods, backward uniqueness
17/03/2011:	Wave equation: D'Alembert's formula, energy methods
22/03/2011:	Midterm review
24/03/2011:	Midterm Exam
29/03/2011:	Midterm return and discussion
31/03/2011:	Introduction to scalar conservation laws (begin)
05/04/2011:
07/04/2011:
12/04/2011:
14/04/2011:
26/04/2011:
28/04/2011:
03/05/2011:
05/05/2011:	Presentation
10/05/2011:	Presentation
12/05/2011:	Review for final exam
TBA:	Final Exam

Last modified: 2011/02/09
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2011/math362/index.html
Marcel Oliver (m.oliver@jacobs-university.de)

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