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DN1215 Numerical Methods, Basic Course 7.5 credits

Numeriska metoder, grundkurs

Basic course in numerical methods.

  • Educational level

    First cycle

  • Academic level (A-D)

    A

  • Subject area

    Techonology

  • Grade scale

    A, B, C, D, E, FX, F

Course offerings

Spring 13 numme for programme students

Learning outcomes

An overlying goal with the course is the realization of the necessity of numerical methods in order to simulate technological and scientific processes based on mathematical models.

After completing this course, the students should be able to

  • identify various mathematical problems and reformulate these in a way suitable for numerical treatment
  • select a suitable numerical method for the treatment of the given problem
  • motivate the choice of a method by describing its advantages and limitations
  • select an algorithm leading to efficient computation and implement this in a programming language, suitable for scientific computing, e.g. Matlab
  • present the results in a relevant and illustrative way
  • provide an estimate of the accuracy of the results
  • utilize standard functions from e.g. Matlab's library for calculation, visualization and efficient programming.

Course main content

Basic concepts and ideas: algorithm, local linearization, iteration, extrapolation, discretization, convergence, stability, condition.

Reliability assessment: parameter sensitivity, experimental perturbations, precision.

Numerical methods for: linear and nonlinear systems of equations, interpolation, model-fitting with the method of least squares, optimization, quadrature. Methods for systems of ordinary and some partial differential equations, initial value problems, boundary value problems and methods for Fourier analysis.

The application of mathematical software in the solution of scientific and engineering problems, numerical experimentation, and the presentation of effective algorithms.

Eligibility

Prerequisites

Mandatory first year courses in mathematics and a course in computer science or programming.

Literature

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

T. Sauer: Numerical Analysis, Pearson 2006.

Examination

  • LAB1 - Laboratory Work, 2.5 credits, grade scale: P, F
  • PRO1 - Project, 2.5 credits, grade scale: P, F
  • TEN1 - Examination, 2.5 credits, grade scale: A, B, C, D, E, FX, F

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Requirements for final grade

Examination (TEN1; 2,5 hp) Laboratory assignments (LAB1; 2,5 hp) Project (PRO1; 2,5 hp)

Offered by

SCI/Mathematics

Contact

Jesper Oppelstrup, e-post: jespero@kth.se

Examiner

Jesper Oppelstrup <jespero@kth.se>

Supplementary information

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Add-on studies

2D1220/DN2220 Applied Numerical Methods I or 2D1250 /DN2250 Applied Numerical Methods II, 2D1225 /DN2225 Numerical Solution of Differential Equations I, 2D1266 /DN2266 Mathematical Models, Analysis and Simulation, Part I or 2D1252/DN2252 Numerical Algebra, 2D1264/DN2264 Parallel Computations for Large-Scale Problems part 1.

Version

Course plan valid from: Autumn 09.
Examination information valid from: Spring 08.