Syllabus for Scientific Computing II

Learning outcomes

Upon completion of the course, 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 the properties in algorithms and mathematical models and, based on the evaluation discuss the suitability of these methods given an application problem;
• solve problems in science and engineering by breaking the problem into sub-problems, use software efficiently and write code using a good programming standard;
• present, explain, summarise, evaluate and discuss solution methods and results in a report.

Content

Programming in MATLAB and methodology for problem solving. Solution to ordinary differential equations (initial-value problem). Adaptivity. Stability. Explicit and implicit methods. Order of a method, order of accuracy. Monte Carlo methods and methods based on random number, stochastic models, stochastic simulation, stochastoc ordinary differential equations, inverse transform sampling.

Key concepts covered in the course: discretisation and discretisation error (truncation error), accuracy and order of accuracy, local and global error, efficiency, stability and instabilty, adaptivity, stiff and non-stiff ordinary differential equations, deterministic/stochastic models and methods.

Instruction

Lectures, problem classes, laboratory work, mini projects.

Assessment

Written examination (3 credits). Written report on mini project and problem sovling tasks (2 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.