Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2013-11-15
Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMA250
Teaching language: English
The probably largest class of mathematical models among technichal systems is based on partial differential equations (PDE). An indispensable tool in the modern theory for these equations is distribution theory. The aim of the course is on the one hand to give a more stable theoretical foundation for concepts and methods for PDEs that have been introduced in earlier courses, and a greater ability to independently use these, and on the other hand to develop the theory further. Moreover, the course aims to give the analytical background to some frequently used numerical solution methods.
Knowledge and Understanding
For a passing grade the doctoral student must
Competences and Skills
For a passing grade the doctoral student must
Distribution theory: derivatives, convergence, fundamental solutions, Green's functions, the Fourier transform, the Laplace and the wave operators. Partial differential equations: spectral methods, eigenfunction expansions, weak solutions. Approximation methods. Integral equations, finite element methods. Geometrical methods. Characteristics. The study of some model equations.
Renardy, M. & Rogers, Robert C.: An Introduction to Partial Differential Equations. Springer, 2004. ISBN 9780387004440.
Material distributed by the department.
Types of instruction: Lectures, laboratory exercises, exercises
Examination formats: Written exam, oral exam, written assignments.
Written and/or oral test, to be decided by the examiner. Written assignments.
Grading scale: Failed, pass
Examiner:
Assumed prior knowledge: FMA021, first part of FMA260.
Course coordinators:
Web page: http://www.ctr.maths.lu.se/course/partdiff/