Entry requirements

BSc degree of which at least 30 credits in mathematics, 5 credits computer programming and 5 credits scientific computing.

Learning outcomes

To pass, the student should be able to

• describe the key concepts covered in the course (see Content);
• in general terms explain the ideas behind the algorithms that are presented in the course;
• evaluate methods with respect to accuracy, stability properties and efficiency;
• describe the fundamental difference between stochastic and deterministic algorithms;
• use computational software and write minor programs using that software;
• 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 written report.

Content

MATLAB, programming in MATLAB, use of Comsol Multiphysics. Solutions to linear systems of equations using LU-decomposition. Matrix and vector norms. The concepts sensitivity, conditioning, stable/non-stable algorithm. Solutions to ordinary differential equations (initial value problems). Adaptivity. Stability. Explicit and implicit methods and solutions to non-linear systems of equations. The concepts of discretisation and discretisation (truncation) error, iteration and linearisation. Floating point representation and the IEEE floating-point standard, machine epsilon and rounding error. Monte Carlo methods and methods based on stochastic simulation. Partial differential equations. Methods based on finite differense methods and finite element methods. Basic iterative methods for linear systems of equations.

Key concepts covered in the course: discretisation and discretisation error, machine epsilon, condition and condition number, accuracy and order of accuracy, efficiency, consistency, stability, ansatz, adaptivity, convergence.

Instruction

Lectures, problem classes, laboratory work and compulsory assignments.

Assessment

Written examination at the end of the course and approved compulsory assignments.

Other directives

The aim of the Scientific Computing, bridging course is to provide students with the knowledge required for the study of higher courses in Scientific Computing or Computational Science. The course assist in bridging the gap between previous Scientific Computing studies and the level needed at the Master in Computational Science. As a prerequisite this course can replace Scientific computing III.