autumn 2011

MAT-2201 Numerical Methods - 10 stp

Numerical Methods
The course is administrated by
Fakultet for naturvitenskap og teknologi
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.
Recommended prerequisites
MAT-1003 Calculus 3, MAT-1004 Linear algebra
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 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: 40 h
Coursework: 30 h
Assessment methods
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.
Date for examination
Skriftlig eksamen: 14.12.2011
The date for the exam can be changed. The final date will be announced at your faculty early in May and early in November.
Skriftlig eksamen
Course overlap
MA-224 Numerical calculations 10
FYS-2011 Numerical simulations 10
Recommended reading/syllabus


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

Lectures Autumn 2011
First attendance: Tue 23rd of Aug, 14:15 at B203, Realfagbygget
Lectures Prof. Einar Mjølhus