Syllabus academic year 2011/2012

(Created 2011-09-01.)

**Credits:** 6.
**Grading scale:** TH.
**Cycle: ** G2
(First Cycle).
**Main field: **Technology.
**Language of instruction: **The course will be given in English on demand.
**FMN050 overlaps following cours/es: **FMN011, FMN041, FMN081, FMN130, FMNF01 and FMNN10.
**Compulsory for:** E3.
**Alternative for:** I3.
**Course coordinator:** Director of studies Anders Holst, Anders.Holst@math.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 assignments and a written exam.
**Home page:** http://www.maths.lth.se/education/lth/courses/numan/2012/.
**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 using computers forms a central part of the course.

*Knowledge and understanding*

For a passing grade the student must

be able to choose suitable computational methods to solve simple problems that occur in mathematical models in, e.g., electronics, and to be able to construct computable approximations. Moreover, students must be able to independently implement and to apply such algorithms.
*Skills and abilities*

For a passing grade the student must

- be able to independently select and apply computational algorithms using a computer, and be able to evaluate both accuracy and relevance of the 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**

Software for scientific computing, error analysis, computer arithmetic, condition number, systems of linear equations, method of least squares, calculation of eigenvalues, solution of nonlinear equations using fixed point or Newton iterations, interpolation, ordinary differential equations, basic signal processing using FFT.

**Literature**

Timothy Sauer: Numerical Analysis. Pearson Education (2007), ISBN 9780321461353