Course contents *

Review and deepening of the basic course. Optimization in one and several variables. Geometric modeling in 2D and 3D using splines and Bezier curves.

Numerical linear and nonlinear algebra, sparse matrices, direct and iterative methods for solving linear systems of equations.eigenvalue algorithms, QR-factorization, SVD with applications. Discrete fourier transform with applications. Linear and nonlinear least-squares fitting. Boundary value problems and eigenvalue problems for ordinary differential equations. Finite difference methods and Galerkin's method. Explicit and implicit methods for initial value problems for ordinary differential equations. Stability and stiff problems.

Numerical treatment of partial differential equations, algorithms for parabolic, elliptic and hyperbolic problems.

Intended learning outcomes *

An overall aim with this second course is to give the student knowledge about how to formulate, use, and implement computer oriented numerical methods to solve problems from different areas of application

After having taken the course the student shall be able to

- identify problem type of a practical numerical problem

- know how such a computation should be performed, choose suitable algorithm, estimate the computer resources needed and judge the quality of the result

- implement the algorithms in a computer language suitable for numerical computation, e.g. Matlab

- use computer tools for simulation and visualization in science and engineering

Course Disposition

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Specific prerequisites *

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Recommended prerequisites

A basic course in numerical methods, 2D1212/DN121 or 2D1214/DN1214 or 2D1240/DN1240.

Equipment

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Literature

To be announced at least 2 weeks before course start at course web page. Previous year:

G. Eriksson, Kompendium i tillämpade numeriska metoder

C. Moler, Numerical computing with Matlab, SIAM 2004

T. Sauer, Numerical analysis, Pearson 2006

Grading scale *

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

Examination *

• LAB1 - Laboratory Task and Project 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.

Other requirements for final grade *

Written exam (TENl; 3 university credits).
Computer assignments (LAB1; 3 university credits.).

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

Jesper Oppelstrup

Course web

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Offered by

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

2D1225/DN2225 Numerical treatment of differential equations, 2D1260/DN2260 Finite element method, 2D1264/DN2264 Parallel computation for large scale problems.

Contact

Lennart Edsberg, tel: 790 8119, e-post: edsberg@nada.kth.se

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.

Supplementary information

This course cannot be counted in the degree if the student has taken 2D1251/DN2251.

Replaces 2D1220.

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.