# Scientific Computing

### Course content

This course focuses on the general techniques and ideas found in professionally written numerical software, as well as the general concepts one needs to know for applying suitable software in a qualified manner to computational problems. Thus, the course is aimed much more at potential users of mathematical software than at potential creators of such software.

Education

MSc Programme in Nanoscience

MSc Programme in Physics

Learning outcome

Skills
At course completion, the student should be able to:

• Choose an appropriate numerical method for the solution of the problem or sub-problem. The numerical method is selected among the methods presented in the course and it should be chosen with respect to the requirements of the model.
• Evaluate the numerical method with respect to potential accuracy, computational efficiency, robustness and memory requirements.
• Perform the required computation using Matlab or similar systems.
• Evaluate the quality of the solution with respect to the accuracy obtained and the sensitivity to model parameter variations.
• Estimate whether the quality of the solution is adequate relative to the desired use of the model.
• Analyse the reasons of a possible total failure of a method applied to a concrete problem.

CompetencesThe methods presented in the course enable the student to perform numerical analysis of simple mathematical models from science in order to solve concrete problems and to evaluate the results obtained. The solution will mainly be based on Matlab or similar systems.

Knowledge
Presentation and numerical analysis of simple mathematical models from science. Presentation of ideas behind and motivation for fundamental numerical methods for the solution of: linear and nonlinear equations, linear and nonlinear optimization, eigenvalue problems, initial value problems for ordinary differential equations, partial differential equations and the fast Fourier transform.

Lectures, exercises and 4 small projects. Duration 9 weeks.

Michael T. Heath: Scientific computing. An introductory survey, 2nd ed. from McGraw-Hill.

Corresponding to the courses MatIntro and LinAlg. Programming ability is also required . Further more ability corresponding to at least one of the following prerequisites: An1, MatF, 1st year computer science.

Restricted elective for specialisation "Physics".
It is expected that the student brings a laptop
Necessary software:
Windows: Xming
Xming:http:/​/​sourceforge.net/​projects/​xming/​ & http:/​/​www.straightrunning.com/​XmingNotes/​
Linux:X11 runs automatically
X11 is a part of OS X in Leopard and Lion.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Independent evaluation of 4 projects. The final grade is the average of the grades of each of the 4 projects.
Marking scale
Censorship form
No external censorship
More internal examiners
##### Criteria for exam assessment

See Skills.

Single subject courses (day)

• Category
• Hours
• Lectures
• 32
• Practical exercises
• 16
• Project work
• 100
• Preparation
• 58
• English
• 206