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.