autumn 2018
MAT2201 Numerical Methods  10 stp
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 MAT1003 Calkulus 3 and MAT1004 Linear algebra or equal.
Application code: 9336 (Nordic applicants).
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, roundoff 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.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 IEEEstandards for binary number representation
 Be able to use iterative methods, like the Jacobimethod for systems of linear equations, and Newtons method for nonlinear 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.
Assessment
Written final exam of 4 hours duration, counting 100 %.
Assessment scale: Letter grades AF.
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.
Date for examination
Written test 05.12.2018The date for the exam can be changed. The final date will be announced in the StudentWeb early in May and early in November.
Schedule
Recommended reading/syllabus
Curriculum for MAT2201 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):
ISBN13: 9780321783677
ISBN10: 0321783670
or International edition (alternative 2):
ISBN13: 9781292023588
or new version (the one for sale in Akademika)
T. Sauer: Numerical Analysis. 3rd edition. Pearson:
ISBN13: 9780134696454
ISBN10: 013469645X
Ch. 0. Fundamentals
Ch. 1. Solving equations
1.1 The bisection method
1.2 Fixedpoint 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 NewtonCotes formulas (except 5.2.4 open NewtonCotes 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 RungeKutta 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 "pNorm of vectors and matricesForhåndsvis dokumentet" is also a part of the syllabus
Appendix BForhåndsvis dokumentet (for those who use MATLAB): Introduction to MATLAB
Lectures Autumn 2018 First attendance: Mon 20th Aug, 10:15, Lille aud., Realfagbygget 

Lectures 
f.aman. HegeBeate Fredriksen 