Scientific Computing I

5 credits

Syllabus, Bachelor's level, 1TD393

A revised version of the syllabus is available.
Code
1TD393
Education cycle
First cycle
Main field(s) of study and in-depth level
Computer Science G1F, Mathematics G1F, Technology G1F
Grading system
Pass with distinction, Pass with credit, Pass, Fail
Finalised by
The Faculty Board of Science and Technology, 3 May 2010
Responsible department
Department of Information Technology

Learning outcomes

To pass, the student should be able to

  • describe the concepts algorithm, numerical method, discretisation and discretisation error, accuracy and order of accuracy, stable/unstable algorithm, machine epsilon, iteration, condition and condition number, efficiency, adaptivity, convergence;
  • perform a minor analysis of computational problems in order to answer questions related to the concepts stated in previous item;
  • in general terms explain the ideas behind the algorithms that are presented in the course and how they can be used for solving problems an application areas;
  • describe the methodology used in numerical computations compared with analytical solutions, and the effect of floating point representation and discretisation ;
  • in problem solving use fundamental programming structures (if, while, for) in algorithms and programming code
  • given a computational problem, structure and divide into sub-problems, formulate an algorithm and implement the algorithm in MATLAB;
  • explain simple programming code in MATLAB and write well-structured small size programs by means of script files and self-written functions;
  • in a short report explain and summarise solution methods and results in a lucid way

Content

MATLAB and programming in MATLAB: basic programming structures (if, for and while structure), functions and sub-programs, parameter passing. The program structure, the algorithm concept. Problem solving methodology. Given a problem, divide it into sub-problems, write an algorithm and transform the algorithm to a computer program.

Solution to linear equation systems using LU-factorisation. Norms for matrices and vectors. Sensitivity and condition number, stable/unstable algorithm. Numerical solution to integrals. The concepts discretisation and discretisation error. Solution to non-linear equations and the concepts iteration and linearisation. Floating point representation and the IEEE-standard for floating point arithmetic, machine epsilon and the round-off error.

Key concepts covered in the course: algorithm, numerical method, discretisation och discretisation error, accuracy and order of accuracy, stable and unstable algorithm, machine epsilon, iteration, condition and condition number, efficiency, adaptivity, convergence.

Instruction

Lectures, problem classes/workouts, laboratory work, compulsory assignments/mini projects.

Assessment

Written examination at the end of the course and compulsory assignments/mini projects.

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