(Created 2008-07-17.)
 NUMERICAL METHODS IN PHYSICS AND ENGINEERING FMN041

Higher education credits: 6. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in English on demand. FMN041 overlap following cours/es: FMN011, FMN050, FMN081, FMN130, FMN011, FMN050, FMN081 och FMN130. Compulsory for: F3. Course coordinator: Achim Schroll, Achim.Schroll@na.lu.se, Numerisk analys. Recommended prerequisits: FMA420 Linear Algebra, FMA410 Calculus in One Variable, FMA430 Calculus in Several Variables, experience with MATLAB. Assessment: The grade is based on homework assignments and a written exam. Home page: http://www.maths.lth.se/na/courses/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

Mathematical models are often written as systems of linear and nonlinear equations and differential equations. Students are expected to discretize such equations, that is to construct computable approximations. Moreover, students have to implement and to apply such algorithms independently

Skills and abilities
For a passing grade the student must

- be able to independently select and apply computational algorithms

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

Judgement and approach
For a passing grade the student must

- report solutions to problems and numerical results in written form.

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

- write an 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