DN2251 Applied Numerical Methods III 9.0 credits

A second course in numerical methods consisting of the first part of 2D1252/DN2252, numerical algebra and 2D1225/DN2225, numerical treatment of differential equations I. Together this corresponds to 2D1250/DN2250, applied numerical methods II. The course is a part of the first year of study for the international master program in Scientific Computing.

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Content and learning outcomes

Course contents *

Numerical Algebra:

Linear systems of equations: direct algorithms, perturbation theory and condition, rounding errors. Sparse matrices. Iterative methods: stationary iterations, Krylov space methods and preconditioning.

Eigenvalue problems: Theory, transformation methods and iterative methods.

Singular value decomposition and its applications.

Nonlinear systems of equations and numerical optimization. Model fitting.

Differential equations:

Numerical treatment of initial value problems, boundary value problems, and eigenvalue problems for ordinary and partial differential equations. Discretization by finite differences, finite elements, and finite volumes. Convergence, stability and error analysis.

Application oriented computer labs and a project.

Intended learning outcomes *

An overall aim with this course is to give the student knowledge about how to formulate, use, analyse and implement advanced computer oriented numerical methods to solve problems in numerical algebra and differential equations from different application areas.

After completing the course the student should be able to

1) in numerical algebra

- identify algebra computations, linear and nonlinear, in a practical problem

- implement such a computation, estimate computer resource needs and judge the quality of the results.

- implement special numerical algorithms adapted to the properties of the problem

2) in numerical solution of differential equations

- for a given problem, identify problem type within the area of differential equations, ordinary and partial, and suggest an algorithm for the numerical solution

- utilise and analyze the most important algorithms for the kind of problems presented in this course

- utilise those algorithms from other areas of numerical analysis which are necessary for solving differential equations, e.g. large sparse linear systems of equations, Fourier analysis, etc

- set up and explain some fundamental mathematical models in science which are based on differential equations

- implement the algorithms i a programming language suitable for numerical computation, e.g. Matlab

- utilise computer tools for simulation and visualization of differential equation models in science and engineering.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

No information inserted

Recommended prerequisites

Basic numerical analysis, equivalent to 2D1210 or 2D1240/DN1240 Numerical Methods basic course I or II.

Equipment

No information inserted

Literature

To be announced at least 2 weeks before the course starts at the web page for the course.

Examination and completion

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

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

Examination *

• LABA - Laboratory Work, 1.5 credits, Grading scale: P, F
• LABB - Laboratory Work, 3.0 credits, Grading scale: P, F
• TENA - Examination, 1.5 credits, Grading scale: A, B, C, D, E, FX, F
• TENB - 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 *

Examination of first part (TEN1; 3 university credits) from course 2D1252/DN2252.
Examination (TEN2; 3 university credits) from course 2D1225/DN2225.
Computer assignments and project work (LAB1; 3 university credits.) from course 2D1225.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

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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

No information inserted

SCI/Mathematics

Main field of study *

No information inserted

Education cycle *

Second cycle

2D1253/DN2253 Numerical algebra, methods for large matrices, 2D1255 /DN2255 Numerical Solution of Differential Equations II, 2D1260 /DN2260 The Finite Element Method, 2D1263 Scientific Computing, 2D1280 Computational Fluid Dynamics, 2D1290 /DN2290 Advanced Numerical Methods.

Contact

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

Supplementary information

The course cannot be counted in the degree if the student has taken 2D1220/DN2220.

The course replaces 2D1251.

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.