Syllabus academic year 2011/2012
(Created 2011-09-01.)
NUMERICAL ANALYSISFMN011
Credits: 6. Grading scale: TH. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. FMN011 overlaps following cours/es: FMN041, FMN050, FMN081, FMN130, FMNF01 and FMNN10. Compulsory for: D3. Optional for: C4. Course coordinator: Carmen Arevalo, carmen@maths.lth.se and Anders Holst, ah@maths.lth.se, Numerical Analysis. 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

- be able to construct computable approximations of mathematical models which are common in science and engineering.

- be familiar with numerical algorithms to handle the above approximations.

- be able to independently implement and apply such algorithms, using mathematical software, e.g. Octave or Matlab.

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, computation of eigenvalues. Discrete Fourier transforms, discrete cosine transforms.

Literature
Sauer, T: Numerical Analysis. Pearson 2007, ISBN 978-0321461353.