PARTIAL DIFFERENTIAL EQUATIONS

Lecturer: P.A. Markowich, MT2009

Introduction

The theory of partial differential equations is a very active area of research in both pure and applied mathematics with many basic questions still unresolved. It is fundamental in mathematical physics and its importance in the rest of applied mathematics is growing enormously. It is also a major area of pure mathematics, and has far reaching connections in topology and geometry. In this course, the three basic linear types of partial differential equations (i.e. the heat equation, the wave equation and the Poisson equation) are studied from a theoretical viewpoint. Various techniques are surveyed but emphasis is placed upon the Fourier transform, the theory of distributions and functional analytic methods as tools for constructing weak solutions.

Literature

For Literatur see the following Bibliography. In addition to the sets of lecture notes written by previous lecturers ([1],[2]) the books [3], [5] are very good for PDE topics in the course. For distributions [4] is most relevant.

## Bibliography

- 1
- T.W. Körner, Cambridge Lecture notes on PDE,
*available at http://www.dpmms.cam.ac.uk/~twk.* - 2
- M. Joshi and A. Wassermann, Cambridge Lecture notes on PDE,
*available at http://www.damtp.cam.ac.uk/user/dmas2.* - 3
- L.C. Evans, Partial Differential Equations,
*AMS Graduate Studies in Mathematics Vol 19, QA377.E93 1990* - 4
- F.G. Friedlander, Introduction to the Theory of Distributions,
*CUP 1982, QA324.* - 5
- Rafael Jos Iorio and Valria del Magalhes Iorio, Fourier Analysis and Partial Differential Equations,
*CUP 2001, QA403.5.I57 2001.*

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Example Sheets

If there are any questions or remarks, please write to jfp37@cam.ac.uk.

Example Sheet I

Example Sheet II

Example Sheet III

Example Sheet IV