Chapter 0. Introduction1. Mathematical modellingChapter 1. Finite Difference Method

2. Analytic properties of partial differential equations

3. Discretization

4. Time-dependent problemsChapter 2. Finite Element Method

5. Finite Differences for the Poisson equation

6. Non-linear problems

7. Approximation of solutions

8. Basic ideas of the Finite Element method

9. The Finite Element method for the Poisson equation

## Prerequisites

Analysis, linear algebra. Some basic knowledge in numerical analysis and the analytic theory of partial differential equations is useful.## Literature

For the background in real analysis, numerical analysis and partial differential equations:

E. DiBenedetto, Real Analysis, Birkhäuser, Boston, 2002.

W. Gautschi, Numerical Analysis, Birkhäuser, Boston, 1997.

E. DiBenedetto, Partial Differential Equations, Birkhäuser, Boston, 1995.A printed manuscript is available for the students of the course including an annotated list of references.

A. M. Hinz, andreas.hinz@mathematik.uni-muenchen.de, 2002-11-21