SF1541 Numerical Methods, Basic Course 7.5 credits

Basic ideas and concepts: algorithm, local linearisation, iteration, extrapolation, discretisation, convergence, stability, condition.

Estimation of reliability: parameter sensitivity, experimental perturbation calculation, precision.

Numerical methods for: linear systems of equations, nonlinear equations and systems of equations, interpolation, model adaptation with the least squares method, optimisation, integrals and differential equations.

Using mathematical software to solve engineering mathematical problem, make numerical experiments and present efficient algorithms.

A general aim with the course is to give the student the understanding that numerical methods are needed to make reliable and efficient simulations of technical and scientific processes based on mathematical models.

On completion of the course, the student should be able to

• identify different mathematical problems and reformulate them in a way that is appropriate for numerical treatment
• choose appropriate numerical method for treatment of the given problem
• explain choice of method by accounting for advantages and limitations
• choose an algorithm that implies efficient calculations and implement it in a programming language, suited for calculations, e.g. Matlab
• present the results in a relevant and illustrative way
• estimate the reliability of the results
• use functions from the programming language library for efficient calculations and visualisation

For non-program students: basic university qualification and 15 credits in mathematics and 6 credits computer science or programming techniques.

G. Eriksson: Numeriska algoritmer med Matlab, CSC/Nada 2002.

T. Sauer: Numerical Analysis, Pearson 2006.

If the course is discontinued, students may request to be examined during the following two academic years.

• LABA - Laboratory Work, 1.5 credits, grading scale: P, F
• LABB - Laboratory Work, 3.0 credits, grading scale: P, F
• TEN1 - Examination, 3.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

· LABA - Laboratory sessions, 1.5 credits, grading scale: P, F

· LABB - Laboratory sessions, 3.0 credits, grading scale: P, F

· TEN1 - Examination, 3.0 credits, grading scale: A, B, C, D, E, FX, F

In this course, the code of honour of the school is applied, see: http://www.sci.kth.se/institutioner/math/avd/na/utbildning/hederskodex-for-studenter-och-larare-vid-kurser-pa-avdelningen-for-numerisk-analys-1.357185

A written examination (TEN1; 3 credits).
Laboratory assignments (LABA; 1.5 credits).
Laboratory assignments with oral and written presentation (LABB; 3 credits).

Katarina Gustavsson

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

DN2220 Applied Numerical Methods I or DN2250 Applied Numerical Methods II, DN2225 Numerical Solution of Differential Equations I, DN2266 Mathematical Models, Analysis and Simulation, Part I or DN2252 Numerical Algebra, DN2264 Parallel Computations for Large-Scale Problems part 1.

The course cannot be counted towards the degree if the student also has taken any of the courses 2D1210, 2D1212/DN1212, 2D1213/DN1213, 2D1214/DN1214, DN1215, 2D1240/DN1240.