Course syllabus

# Partiella differentialekvationer med distributionsteori

Partial Differential Equations with Distribution Theory

## FMA250, 7,5 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Partial Differential Equations with Distribution Theory

Valid for: 2016/17

Decided by: Education Board B

Date of Decision: 2016-03-29

Elective for: F5, F5-bs, Pi4-bs

Language of instruction: The course will be given in English on demand

- 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 student must

- be able to explain the foundations of the theory at an oral examination.
- be able to explain the concept of a weak solution to a PDE, and its connection to distribution theory.

Competences and skills

For a passing grade the student must

- with access to literature independenly be able to integrate methods and views from different parts of the course in order to solve problems and answer questions within the framework of the course.
- in writing and orally, with proper terminology and clear logic be able to explain the solution to a mathematical problem within the course.

*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.

Grading scale: TH

Assessment: Written and/or oral test, to be decided by the examiner. Written assignments.

Required prior knowledge: FMA021 Applied Mathematics, first part of FMA260 Functional Analysis and Harmonic Analysis.

The number of participants is limited to: No

- Renardy & Rogers: An Introduction to Partial Differential Equations. Springer, 2004, ISBN: 0-387-00444-0.
- Material distributed by the department.

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se

Course homepage: http://www.ctr.maths.lu.se/course/partdiff/