# Partial Differential Equations, 7.5 ECTS

Second level## Facts

**Special eligibility requirements**

Knowledge equivalent to 90 credits in mathematics, where Linear Analysis, 7.5 credits, The Foundations of Analysis, 7.5 credits, Analytic Functions I, 7.5 credits, and Ordinary Differential Equations, 7.5 credits, or equivalent, are included. English B/English 6 or equivalent.

## Description

The course covers: Introduction to first order equations. The wave equation: equation in one or several space coordinates, Huygens’ principle. The Laplace equation: fundamental solutions, Green’s function, Dirichlet problem, the maximum principle, Dirichlet’s principle, introduction to Sobolev spaces. The heat equation: initial value problem, fundamental solutions, the maximum principle.

## Area of interests: Science and Mathematics

Science and mathematics help us understand how the world around us is connected – from the origin and structure of the universe, to the development and function of humanity and all other organisms on earth. Scientific knowledge makes it possible to critically examine the credibility of information in different areas of everyday life, society, and the media. As a scientist or mathematician, you will be attractive on a large job market that covers all parts of society and includes everything from pure technology companies to environment and healthcare, as well as research.

## Subject

### Mathematics

As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.