NUMERICAL METHODS IN PHYSICS AND ENGINEERING | FMN041 |

**Aim**

The aim of the course is to teach basics computational methods for solving simple and common mathematical problems by computers and numerical software. This includes the construction, application and analysis of basic computational algorithms. Problemsolving by computers is a central part of the course.

*Knowledge and understanding*

For a passing grade the student must

*Skills and abilities*

For a passing grade the student must

- be able to evaluate both accuracy and relevance of numerical results.

*Judgement and approach*

For a passing grade the student must

- write a logically well structured report in suitable terminology on the construction of basic mathematical models and algorithms.

- write a algorithmically well structured report in suitable terminology on the numerical solution of a mathematical problem.

**Contents**

Linear systems, matrix factirizations and condition, least squares, orthogonal systems, L"-approximation, (Newton-) iteration and order of convergence, interpolation, quadratur, discretization of initial value problems, stiff and non-stiff problems, basics of finite elements, best approximation, error estimates.

**Literature**

Süli, E., Mayers, D. F.: An introduction to Numerical Analysis. 2003. ISBN: 0521007941