Høst 2025

MAT-2201 Numerical Methods - 10 stp

The course is administrated by

Institutt for matematikk og statistikk

Type of course

The course is included in the study programs Applied Physics and Mathematics - master (5-years), Energy, Climate and Environment - master (5-years). It may also be taken independent of study program. This course is also available for inbound exchange students.

Course overlap

FYS-2011 Numerical simulations 10 ects

Course contents

This course gives an introduction to basic concepts and issues of numerical computation. The topics treated include: Binary representation and floating point numbers, round-off errors, conditioning, rates of convergence, truncation and discretization errors, best approximation, numerical stability, and complexity analysis. Selected methods will be covered for some of these classes of problems: Linear systems of equations, nonlinear equations, overdetermined linear systems, numerical differentiation and integration, and numerical solution of differential equations.

Admission requirements

Applicants from Nordic countries:

Generell studiekompetanse og følgende spesielle opptakskrav: Matematikk R1 og i tillegg enten:

Matematikk R2

Fysikk 1 + 2 eller

Kjemi 1+ 2 eller

Biologi 1 + 2 eller

Informasjonsteknologi 1 +2 eller

Geofag 1 + 2 eller

Teknologi og forskningslære 1 + 2

Søknadskode 9197 (kravkode REALFA): Enkeltemner i realfag, lavere grad.

Objective of the course

After the course the student should:

Be able to analyze methods for numerical calculations with respect to errors and complexity
Have mathematical understanding for the methods they apply
Know the main features in IEEE-standards for binary number representation
Be able to use iterative methods, like the Jacobi-method for systems of linear equations, and Newtons method for non-linear equations, and be able to describe convergence properties.
Be able to describe Gaussian elimination and LU factorization, and know QR factorization, and how this is used to find least squares solutions.
Know the problem of polynomial interpolation, how to solve it, and how to prove unqueness. They should be able to use Chebychev polynomials as tools.
Use Taylor¿s theorem to find errors of discretization when calculating dericatives and finite difference.
Know simple methods for numerical calculation of integrals, such as the Trapezoid method and Simpson¿s formula, and general results about global errors, when local errors are known.
Know the simplest algorithms for stepwise numerical solution of initial value problems for systems of first order differential equations, and know how to reformulate a higher order differential equation to such a system.

Language of instruction

The language of instruction and the syllabus is English. Examination questions will be given in English, but may be answered either in English or a Scandinavian language.

Teaching methods

Lectures: Approx 40 h. Coursework: Approx 30 h