Course syllabus

# Partiella differentialekvationer med distributionsteori Partial Differential Equations with Distribution Theory

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

Valid for: 2012/13
Decided by: Education Board 1
Date of Decision: 2011-03-23

## General Information

Elective for: F5, F5-bs, Pi4, Pi4-bs
Language of instruction: The course might be given in English

## Aim

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.

## Learning outcomes

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.

## Contents

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.

## Examination details

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