MAT-2201 Numerical Methods - 10 ECTS
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).
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.
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
A passing grade is required on the mandatory homework sets for permission to take the exam.
Curriculum for MAT-2201 Numerical Methods, autumn 2018
UiT The Arctic University of Norway, Department of Mathematics and Statistics
Textbook: T. Sauer: Numerical Analysis. 2nd edition. Pearson:
US edition (alternative 1):
or International edition (alternative 2):
or new version (the one for sale in Akademika)
T. Sauer: Numerical Analysis. 3rd edition. Pearson:
Ch. 0. Fundamentals
Ch. 1. Solving equations
1.1 The bisection method
1.2 Fixed-point iteration
1.3 Limits of accuracy
1.4 Newton's method
Ch. 2. Systems of equations
2.1 Gaussian elimination
2.2 The LU factorization
2.3 Sources of error
2.4 The PA=LU factorization
2.5 Iterative methods
Ch. 3. Interpolation
3.1 Data and interpolating functions
3.2 Interpolation error
Ch. 4. Least squares
4.1 Least squares and the normal equations
4.2 A survey of models
4.3. QR factorization
Ch. 5. Numerical differentiation and integration
5.1 Numerical Differentiation
5.2 Newton-Cotes formulas (except 5.2.4 open Newton-Cotes methods)
Ch. 6. Ordinary differential equations
6.1 Initial value problem
6.2 Analysis of IVP solvers
6.3 Systems of Ordinary Differential Equations (except 6.3.2 and 6.3.3)
6.4 Runge-Kutta Methods (except 6.4.2 and 6.4.3)
Ch. 7. Boundary value problems
7.1 Shooting Method
7.2 Finite difference methods
Appendix AForhåndsvis dokumentet. Matrix Algebra
Compendium "p-Norm of vectors and matricesForhåndsvis dokumentet" is also a part of the syllabus
Appendix BForhåndsvis dokumentet (for those who use MATLAB): Introduction to MATLAB