# DN2221 Applied Numerical Methods, part 1 6.0 credits

#### Tillämpade numeriska metoder, del 1

Second course in numerical analysis focusing on differential equations.

### Offering and execution

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

## Course information

### Content and learning outcomes

#### Course contents *

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.

#### Intended learning outcomes *

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.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Single course students: 90 university credits including 45 university credits in Mathematics or Information Technology. English B, or equivalent.

#### Recommended prerequisites

Basic numerical analysis equivalent to DN1212 or DN1240.

#### Equipment

No information inserted

#### Literature

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

### Examination and completion

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

#### Examination *

• LAB1 - Laboratory, 3.0 credits, Grading scale: A, B, C, D, E, FX, 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.

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

#### Opportunity to complete the requirements via supplementary examination

No information inserted

#### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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 DN2221

SCI/Mathematics

#### Main field of study *

No information inserted

#### Education cycle *

Second cycle

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

#### Contact

Olof Runborg (olofr@kth.se) ; Lennart Edsberg (edsberg@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

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