Entry requirements

Scientific Computing I. Mathematical Statistics is recommended.

Learning outcomes

To pass, the student should be able to

• describe and perform tasks in connection to the key concepts covered in the course;
• explain the idea behind and apply the algorithms covered in the course;
• explore properties for numerical methods and mathematical models by using the analysis methods covered in the course;
• evaluate algorithms and mathematical models and discuss the suitability of these methods on a given problem;
• 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 report.

Content

Continued programming in MATLAB. Continued problem solving methodology. Data analysis: least squares problems with solution based on the normal equations. Interpolation and piecewise interpolation (including cubic splines). Solution to ordinary differential equations (initial-value problem). Adaptivity. Stability. Explicit and implicit methods. Monte Carlo methods 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, the local and global error, efficiency, stability, adaptivity, stiff and non-stiff ordinary differential equations, deterministic/stochastic models and methods, ansatz, interpolation, least squares.

Instruction

Lectures, problem classes, laboratory work, mini projects.

Assessment

Written examination (3 credits) and approved mini projects (2 credits).