Basic ideas and concepts: algorithm, local linearisation, iteration, extrapolation, discretisation, convergence, stability, condition.
Estimation of reliability: parameter sensitivity, experimental perturbation calculation, precision.
Numerical methods for: linear systems of equations, nonlinear equations and systems of equations, interpolation, model adaptation with the least squares method, optimisation, integrals and differential equations.
Using mathematical software to solve engineering mathematical problem, make numerical experiments and present efficient algorithms.
A general aim with the course is to give the student the understanding that numerical methods are needed to make reliable and efficient simulations of technical and scientific processes based on mathematical models.
On completion of the course, the student should be able to
- identify different mathematical problems and reformulate them in a way that is appropriate for numerical treatment
- choose appropriate numerical method for treatment of the given problem
- explain choice of method by accounting for advantages and limitations
- choose an algorithm that implies efficient calculations and implement it in a programming language, suited for calculations, e.g. Matlab
- present the results in a relevant and illustrative way
- estimate the reliability of the results
- use functions from the programming language library for efficient calculations and visualisation
