Vår 2012

MAT-2201 Numerical Methods - 10 stp

The course is administrated by

Institutt for matematikk og statistikk

Type of course

The course is mandatory in the Master's degree program in industrial mathematics, and is included in the Bachelor's degree program in mathematics and statistics. It may also be taken independent of study program.

Course overlap

FYS-2011 Numerical simulations 10 stp

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, 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.

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. Letter grades (A-F).

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

Recommended reading/syllabus

[LES_MER]
Curriculum for MAT-2201 Numerical Methods, autumn 2011

Textbook: T.Sauer: Numerical Analysis. Pearson 2006

Ch. 0. Fundamentals. The whole chapter

Ch. 1. Solving equations
1.1 The bisection method

1.2 Fixed point iteration
In addition: An extended treatment of iteration, see text "A note on the method of successive approximations" laid out on Fronter.
1.3 Limit of accuracy
1.4 Newton's method

Ch. 2. System of equations
2.1 Gaussian elimination

2.2 The LU factorization
2.3 Sources of error
2.4 The PA=LU factorization
2.5 Interative methods. Confer also the text "A note on the method of successive approximations" referred to above.
2.7.1 Nonelinear systems of equations/Multivariate Newton's method

Ch. 3. Interpolation
3.1 Data and interpolating Functions (exept 3.1.2 Newton's divided differences)
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 Intergration
5.1 Numerical Differentiation
5.2 Newton-Cotes formulas (except 5.2.4 open Newton-Cotes methods)
5.5 Gaussian quadrature

Ch. 6. Ordinary differential equations
6.1 Initial value problem
6.2 Analysis of IVP solvers
6.3 Systems of Ordynary Differential Equations (except 6.3.2 and 6.3.3)
6.4 Runge-Kutta Methods (except 6.4.2 and 6.4.3)
Multistep methods: a simplified discussion of the second order Adam-Bashforth method lectured.

Ch. 7. Bonudary value problems
7.2.1 Finite difference methods/Linear boundary value problems