Syllabus

Scientific Computing, Bridging Course

10 credits

Course code: 1TD044
Established: 2007-03-15
Established by: Teknisk-naturvetenskapliga fakultetsnämnden
Revised: 2009-04-27
Requirements: B.Sc degree where a minimum of 30 ECTS credits mathematics, 5 ECTS credits computer programming and 5 ECTS credits scientific computing is included.
Level of education: Advanced level
Grading System: U Fail, 3 Pass, 4 Pass with credit, 5 Pass with distinction

Main Area of Studies
Computational Science, Computer Science, Mathematics

Learning outcomes

To pass, the student should be able to

• describe the fundamental concepts discretisation and discretisation error, michine epsilon, sensitivity and condition, linearization, accuracy and order of accuracy, efficiency, stability, adaptivity, consistency, convergence;
  


• 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 short report.
  
  

Contents

Matlab and programming in Matlab. 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 discretization and discretization (truncation) error, iteration and linearization. Floating point representation and the IEEE floating-point standard, machine epsilon and rounding error. Monte Carlomethods 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.

Instructions

Lectures, problem classes, laboratory work and compulsory assignments.

Examination

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.