NUMERICAL METHODS IN MECHANICS FMN081

Higher education credits: 7,5. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in English on demand. FMN081 overlap following cours/es: FMN011, FMN041, FMN050, FMN130, FMN011, FMN041, FMN050 och FMN130. Optional for: M2, V3. Course coordinator: Claus Fuhrer, Claus.Fuhrer@na.lu.se, Numerisk analys. Prerequisites: FMA430 Calculus in Several Variables, FMA421Linear Algebra with Computations. The course might be cancelled if the numer of applicants is less than 10. Assessment: The grade is based on homework assignments and a written exam. Home page: http://www.maths.lth.se/na/courses/FMN081/.

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

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

Contents
Polynomial- and spline interpolation, L2 approximation, quadrature, fixed point- and Newton iteration, order of convergence, numerical methods for initial and boundary value propblems, stiff and non stiff problems, consistence and stability, basics of finite elements.

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