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, 3 May 2010
- Responsible department
- Department of Information Technology
Scientific computing I. Mathematical Statistics is recommended.
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;
- in general terms explain the idea behind the algorithms that are presented in the course;
- describe the fundamental difference between stochastic and deterministic methods and models;
- 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. Continued problem solving methodology. Data analysis: least squares problems with solution based on the normal equations. 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, stochastic models, stochastic simulation, inverse transform sampling.
Key concepts covered in the course: discretisation and discretisation error (truncation error), accuracy and order of accuracy, efficiency, stability, ansatz, adaptivity.
Lectures, problem classes, laboratory work, compulsory assignments.
Written examination at the end of the course and compulsory assignments/mini projects.