Syllabus for Scientific Computing, Bridging Course

Learning outcomes

On completion of the course, the student should be able to:

• describe the key concepts covered in the course (see Content) and perform tasks that require knowledge about these concepts,
• in general terms explain the ideas behind, and be able to use algorithms for solving linear systems, ordinary differential equations and for Monte Carlo simulations,
• analyse properties of the computational algorithms and mathematical models using the analytical tools presented in the course,
• discuss suitable methods and algorithms given a application problem,
• 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.

Content

Computational science fundamentals: representation pf floating point numbers, IEEE floating point standard, machine epsilon, rounding errors and its effect on computations. Programming for computations in Python.

Bisic methods för data analysis: regression and the least squares method, Householder transformations and QR decomposition. Numerical solutions to ordinary differential equations (initial value problems): basic numerical methods. Adaptivity. Stability. Explicit and implicit methods. The concepts of discretisation and discretisation (truncation) error. Order of accuracy. Monte Carlo methods and methods based on stochastic simulation: stochastic vs. deterministic methods. Brownian motion and Markov processes. Gillespes algorithm.

Instruction

Laboratory work, lectures, problem and problem solving classes.

Assessment

Written examination of mini project. Problem solving tasks.

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.

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 I and II.

​This course cannot be included in the same degree as 1TD393 Scientific Computing I or 1TD395 Scientific Computing II.