DN2221 Tillämpade numeriska metoder, del 1 6,0 hp

Numerical treatment of initial value problems, boundary value problems, and eigenvalue problems for ordinary and partial differential equations. Discretization by finite differences and finite elements. Convergence, stability and error estimation. Orientation about mathematical modeling. Application oriented computer labs and a project.

An overlying goal with the course is to give the student knowledge about how to formulate, utilise, analyze and implement advanced computer oriented numerical methods for solving those differential equation problems that are of importance in scientific and engineering applications.

After completing this course the student should be able to

• 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 algorithms from other areas of numerical analysis which are necessary for solving differential equations, direct and iterative methods for large sparse systems of equations and Fourier analysis
• 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.

För fristående kursstuderande krävs 90 högskolepoäng varav 45 högskolepoäng inom matematik eller informationsteknik. Dessutom krävs engelska B eller motsvarande.

Basic numerical analysis equivalent to DN1212 or DN1240.

Lennart Edsberg "Introduction to Computation and Modeling for Differential Equations", Wiley 2009.

När kurs inte längre ges har student möjlighet att examineras under ytterligare två läsår.

• LAB1 - Laboration, 3,0 hp, betygsskala: A, B, C, D, E, FX, F
• TEN1 - Tentamen, 3,0 hp, betygsskala: A, B, C, D, E, FX, F

Examinator beslutar, baserat på rekommendation från KTH:s handläggare av stöd till studenter med funktionsnedsättning, om eventuell anpassad examination för studenter med dokumenterad, varaktig funktionsnedsättning.

Examinator får medge annan examinationsform vid omexamination av enstaka studenter.

I denna kurs tillämpas skolans hederskodex, se: http://www.kth.se/csc/student/hederskodex.

Examination (TEN1; 3 hp)
Computer assignments and project work (LAB1; 3 hp)

Olof Runborg

• Vid grupparbete har alla i gruppen ansvar för gruppens arbete.
• Vid examination ska varje student ärligt redovisa hjälp som erhållits och källor som använts.
• Vid muntlig examination ska varje student kunna redogöra för hela uppgiften och hela lösningen.

DN2222 Applied Numerical Methods, part 2, DN2255 Numerical Solutions of Differential Equations, DN2260 The Finite Element Method.

The course replaces DN2225.
This course can be counted in the degree even if the student has taken 2D1255/DN2255.