Fundamental ideas and concepts: algorithm, computational cost, local linearization, iteration, recursion, interpolation, extrapolation, discretization, convergence, stability, condition.
Reliability: parameter sensitivity, perturbation analysis.
Numerical methods: linear and non-linear systems of equations, differential equations, initial-value and boundary-value problems, curve fitting: interpolation and the method of least squares.
An overlying goal with the course is the realization of the necessity of numerical methods in order to simulate technological and scientific processes based on mathematical models.
After completing this course, the students should be able to
- identify various mathematical problems and reformulate these in a way suitable for numerical treatment
- select a suitable numerical method for the treatment of the given problem
- motivate the choice of a method by describing its advantages and limitations
- select an algorithm leading to efficient computation and implement this in a programming language, suitable for scientific computing, e.g. Matlab
- present the results in a relevant and illustrative way
- provide an estimate of the accuracy of the results
- utilize standard functions from e.g. Matlab's library for calculation, visualization and efficient programming