Rand- und Eigenwertprobleme (Summer Semester 2006)
- Lecturer: Prof. Dr. Michael Plum
- Classes: Lecture (1578), Problem class (1579)
- Weekly hours: 4+2
- Audience: Mathematics
The lecture starts on 26th of April, 2006!
|Lecture:||Monday 15:45-17:15||Seminarraum 11|
|Wednesday 11:30-13:00||Seminarraum 34|
|Problem class:||Friday 8:00-9:30||Seminarraum 12|
|Lecturer||Prof. Dr. Michael Plum|
|Office hours: Please get in contact by email.|
|Room 3.028 Kollegiengebäude Mathematik (20.30)|
A boundary value problem consists of an elliptic (or ordinary) differential equation posed on some domain, together with additional conditions required on the boundary of the domain, e.g. prescribed values for the unknown function. Typical origins of boundary value problems are steady-state (i.e. time-independent) situations in physics and engineering.
An eigenvalue problem for a differential equation is a linear and homogeneous boundary value problem depending (typically linearly) on an additional parameter, and one is interested in values of this parameter such that the boundary value problem has nontrivial solutions. Eigenvalue problems arise e.g. after separation of variables in time-dependent problems (thus describing many vibrational situations, including quantum mechanics).
The lecture course addresses students in their fourth semester (second year) or higher, with substantial knowledge in analysis and linear algebra.
The lectures will be accompanied by exercise lessons. Attendance of these exercises is strongly recommended to all participants.
A. Friedman: Partial Differential Equations
(general elliptic PDE of order 2m, but smooth data only)
D. Gilbarg, N. Trudinger: Elliptic Partial Differential Equations of Second Order
(elliptic PDE of second order, mainly Dirichlet b.c.)
L. C. Evans: Partial Differential Equations
R. A. Adams: Sobolev Spaces
(no PDEs, but excellent and general introduction into Sobolev spaces, an essential tool in PDE theory)