Scientific Computing II
Syllabus, Bachelor's level, 1TD395
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Computer Science G1F, Technology G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Information Technology
Scientific computing I.
To pass, the student should be able to
- describe the fundamental concepts discretisation, accuracy and order of accuracy, efficiency, stability, discretisation errors (truncation error), ansatz, adaptivity;
- generally explain the idea behind the algorithms that are presented in the course;
- describe the fundamental difference between stochastic and deterministic algorithms;
- analyse the order of accuracy and stability properties for basic numerical methods and understand how such an analysis is employed;
- evaluate methods with respect to accuracy, stability properties and efficiency;
- based on such evaluation, discuss the suitability of methods given different different applications;
- given a mathematical model, solve problems in science and engineering by structuring the problem, choose appropriate numerical method and generate solution using software and by writing programming code;
- present, explain, summarise, evaluate and discuss solution methods and results in a short report.
Continued programming in MATLAB, with specialisation in visualisation. Continued problem solving methodology. Data analysis: least squares problems with solution based on the normal equations and QR decomposition. Interpolation with an emphasis on piecewise interpolation (including cubic spines). Solution to ordinary differential equations (initial-value problem). Adaptivity. Stability. Explicit and implicit methods and in connection with this solution to non-linear equation systems. Monte Carlometoder and methods based on random number.
Lectures, problem classes, laboratory work, compulsory assignments.
Written examination at the end of the course and compulsory assignments.