# Scientific Computing I

5 credits

Syllabus, Bachelor's level, 1TD393

A revised version of the syllabus is available.
Code
1TD393
Education cycle
First cycle
Main field(s) of study and in-depth level
Computer Science G1F, Mathematics G1F, Technology G1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 12 May 2009
Responsible department
Department of Information Technology

## Learning outcomes

To pass, the student should be able to

• describe the concepts algorithm, numerical method, discretisation and discretisation error, accuracy and order of accuracy, stable/unstable algorithm, machine epsilon, iteration, condition and condition number, efficiency, adaptivity, convergence;
• perform a minor analysis of computational problems in order to answer questions related to the concepts stated in previous item;
• in general terms explain the ideas behind the algorithms that are presented in the course and how they can be used for solving problems an application areas;
• describe the methodology used in numerical computations compared with analytical solutions, and the effect of floating point representation and discretisation ;
• in problem solving use fundamental programming structures (if, while, for) in algorithms and programming code
• given a computational problem, structure and divide into sub-problems, formulate an algorithm and implement the algorithm in MATLAB;
• explain simple programming code in MATLAB and write well-structured small size programs by means of script files and self-written functions;
• in a short report explain and summarise solution methods and results in a lucid way

## Content

MATLAB and programming in MATLAB: basic programming structures (if, for and while structure), functions and sub-programs, parameter passing. The program structure, the algorithm concept. Problem solving methodology. Given a problem, divide it into sub-problems, write an algorithm and transform the algorithm to a computer program.

Solution to linear equation systems using LU-factorisation. Norms for matrices and vectors. Sensitivity and condition number, stable/unstable algorithm. Numerical solution to integrals. The concepts discretisation and discretisation error. Solution to non-linear equations and the concepts iteration and linearisation. Floating point representation and the IEEE-standard for floating point arithmetic, machine epsilon and the round-off error.

## Instruction

Lectures, problem classes/workouts, laboratory work, compulsory assignments/mini projects.

## Assessment

Written examination at the end of the course and compulsory assignments/mini projects.