autumn 2020
MAT-2201 Numerical Methods - 10 ECTS

Last changed 11.08.2021

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 - nokut.no

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

Application code: 9336 (Nordic applicants).


Course overlap

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

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

Assessment

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
  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: MAT-2201