FMA145F

Temporary

Partial Differential Equations

7.5

Course given jointly for second and third cycle

7151 (Centre of Mathematical Sciences / Mathematics)

 -04-24

Professor Thomas Johansson

English

If sufficient demand

The aim of is to give a thorough introduction to the modern mathematical theory for the partial differential equations that are of greatest importance in physics. For this purpose an introduction to the theory of distributions and the theory of Sobolev spaces.

Quasi-linear equations of the first order. Classification of second-order equations. The Cauchy-Kowalevski theorem. The Holmgren uniqueness theorem. The Laplace equation. The wave equation. The heat equation.

be able to account for the basics of distribution theory and the theory of Sobolev spaces.

be able to describe the three main classes of second order equations: elliptic, parabolic and hyperbolic, and describe the properties of their solutions.

be able to formulate and prove the most important theorems.

be able to use the method of characteristics to solve first order linear equations.

be able to explain the concept "well-posed problem" and its importance when modelling with differential equations.

Lectures

Seminars

Written exam

Oral exam

Written assignments

Failed, pass

For admission to the course, English B is required as well as at least 82.5 credits in mathematics in which should be included the courses MATC11 Analytic functions, 15 credits and MATM14 Ordinary Differential Equations, 7.5 credits or the equivalent.

Evans, Lawrence C.: Partial Differential Equations. American Mathematical Soc., 2010. ISBN 9780821849743.

FMA145F

 -04-24

Professor Thomas Johansson