autumn 2019
MAT-2201 Numerical Methods - 10 ECTS

Application deadline

Applicants from Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Applicants from outside the Nordic countries: 1 October for the spring semester and 15 April for the autumn semester.

Type of course

The course is mandatory i the study program Mathematics and Finance - master, and it's included in the study programs Mathematics and Statistics - bachelor and Applied Physics and Mathematics - master (5-years). It may also be taken independent of study program.

Admission requirements

Applicants from Nordic countries: Generell studiekompetanse og følgende spesielle opptakskrav: Matematikk R1 + R2 og i tillegg enten:

  • 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

International applicants: Higher Education Entrance Qualification and certified language requirements in English. It is a requirement that students have  some prior knowledge of biology and ecology, chemistry and mathematics (Participants must have taken introductory level university courses, and achieved pass grades, in these subjects).

A list of the requirements for the Higher Education Entrance Qualification in Norway can be found on the Norwegian Agency for Quality Assurance in Education website -

Recommended prerequsites is MAT-1003 Calkulus 3 and MAT-1004 Linear algebra or equal.

Application code: 9336 (Nordic applicants).

Course overlap

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

MA-224 Numerical calculations 10 stp
FYS-2011 Numerical simulations 10 stp

Course content

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.

Recommended prerequisites

MAT-1002 Calculus 2, MAT-1004 Linear algebra

Objectives 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 and examination

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: 40 h
Coursework: 30 h


Written final exam of 4 hours duration, counting 100 %.

Assessment scale: Letter grades A-F.

Postponed examination:
Students with valid grounds for absence will be offered a postponed examination early in the following semester.

For further details see:
- Utfyllende bestemmelser for eksamener ved Fakultet for naturvitenskap og teknologi (only in Norwegian)
- Regulations for examinations at the University of Tromsø

Coursework requirements
A passing grade is required on the mandatory homework sets for permission to take the exam.

Recommended reading/syllabus

Pensumliste for MAT-2201 Numerical Methods

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  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: MAT-2201
  • Tidligere år og semester for dette emnet