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DN1215 Numerical Methods, Basic Course 7.5 credits

Basic course in numerical methods.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus DN1215 (Autumn 2009–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

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.

Intended 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 disposition

No information inserted

Literature and preparations

Specific prerequisites

No information inserted

Recommended prerequisites

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

Equipment

No information inserted

Literature

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

T. Sauer: Numerical Analysis, Pearson 2006.

Examination and completion

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

Grading scale

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

Examination

  • LAB1 - Laboratory Work, 2,5 hp, betygsskala: P, F
  • PRO1 - Project, 2,5 hp, betygsskala: P, F
  • TEN1 - Examination, 2,5 hp, betygsskala: 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.

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.

Other requirements for final grade

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

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

No information inserted

Ethical approach

  • 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.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web DN1215

Offered by

SCI/Mathematics

Main field of study

Technology

Education cycle

First cycle

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.

Contact

Katarina Gustavsson (katg@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.