autumn 2024
MAT-2201 Numerical Methods - 10 ECTS

  1. Startsida
  2. Emnekatalog
  3. Numerical Methods

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.

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

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 ects
FYS-2011 Numerical simulations 10 ects

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: Approx 40 h. Coursework: Approx 30 h

Information to incoming exchange students

This course is open for inbound exchange student who meets the admission requirements, including prerequisites. Please see the Admission requirements" and the "Prerequisite" sections for more information.

Do you have questions about this course? Please check the following website to contact the course coordinator for exchange students at the faculty: https://en.uit.no/education/art?p_document_id=510412

Schedule

Se timeplan

Examination

Examination: Date: Duration: Grade scale:
School exam 03.12.2024 09:00
 4 Hours A–E, fail F

Coursework requirements:

To take an examination, the student must have passed the following coursework requirements:
Mandatory homework sets Approved – not approved
UiT Exams homepage

Re-sit examination

Students having failed the last ordinary examination are offered a re-sit examination early in the following semester.
  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: MAT-2201
  • Tidligere år og semester for dette emnet