# Scientific Computing II

5 credits

Syllabus, Bachelor's level, 1TD395

Code
1TD395
Education cycle
First cycle
Main field(s) of study and in-depth level
Computer Science G1F, Technology G1F
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

## Entry requirements

Scientific computing I. Mathematical Statistics is recommended.

## Learning outcomes

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.

## Content

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.

## Instruction

Lectures, problem classes, laboratory work, compulsory assignments.

## Assessment

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