Basic concepts and ideas: algorithm, local linearization, iteration, extrapolation, discretization, convergence, stability, condition.
Reliability assessment: parameter sensitivity, experimental perturbations, precision.
Numerical methods for: linear and nonlinear systems of equations, interpolation, model-fitting with the method of least squares, optimization, quadrature. Methods for systems of ordinary and some partial differential equations, initial value problems, boundary value problems and methods for Fourier analysis.
The application of mathematical software in the solution of scientific and engineering problems, numerical experimentation, and the presentation of effective algorithms.
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.
