Syllabus academic year 2009/2010

(Created 2009-08-11.)

**Higher education credits:** 6.
**Grading scale:** TH.
**Level: ** G2
(First level).
**Language of instruction: **The course will be given in English on demand.
**FMN011 overlap following cours/es: **FMN041, FMN050, FMN081, FMN130, FMN041, FMN050, FMN081, FMN130, FMN041, FMN050, FMN081, FMN130, FMNF01, FMNN10, FMN041, FMN050, FMN081, FMN130, FMNF01 och FMNN10.
**Compulsory for:** D3.
**Optional for:** C4, L4gi.
**Course coordinator:** Carmen Arevalo, carmen@maths.lth.se, Numerisk analys.
**Recommended prerequisits:** FMA420 Linear Algebra, FMAA01/05 Calculus in One Variable, FMA430 Calculus in Several Variables, experience with MATLAB.
**Assessment:** The grade is based on homework reports and a written exam.
**Home page:** http://www.maths.lth.se/na/courses/FMN011.
**Aim**

The aim of the course is to teach basic computational methods for solving simple and common mathematical problems using computers and numerical software. This includes the construction, application and analysis of basic computational algorithms. Problem solving with 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.

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

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

**Contents**

Error analysis, numerical methods for systems of (non-) linear equations, least squares method, polynomial interpolation, splines, Bezier curves, numerical integration, ordinary differential equations, computation of eigenvalues.

**Literature**

Timothy Sauer: Numerical Analysis. Pearson (2006), ISBN 0-321-26898-9