| Credits |
8 credit points |
| Instructors |
Vorst, R.C.A.M. van der (Vrije Universiteit) |
| E-mail |
RCAM.van.der.Vorst@few.vu.nl |
| Aim |
The aim of this course is to obtain a basic knowledge of the theory of PDEs (elliptic, parabolic and hyperbolic). Participants will be introduced to classical techniques, as well as to Hilbert space methods. Developing practical skills by which PDEs can be studied is a second important aspect of the course. |
| Description |
The first PDEs encountered in this course are - linear - first order equations. We discuss a classification of linear
PDEs of any order - mainly constant coefficients. We start with an introduction to PDEs via Fourier series methods.
These methods are motivated via the classical examples of hyperbolic (wave), parabolic (diffusion) and elliptic (Laplace) equations. A brief introduction to Sobolev spaces and Hilbert space methods accumulates in the proof of the existence of weak solutions of linear elliptic equations by the Lax-Milgram Lemma, as well as some basic regularity theory. Furthermore, eigenvalue problems and expansions of eigenfunctions are studied through these methods. |
| Examination |
Based on take home exercise series. |
| Literature |
L.C. Evans: Partial differential equations, GSM 19, American mathematical society
* 'Lectures Notes' on Partial Differential Equations' by A. Doelman |
| Prerequisites |
A basic knowledge real and complex analysis and/or calculus. A background in ordinary differential equations and/or dynamical systems. |
