After successful completion of the course, students are able to solve basic numerical tasks in areas such as interpolation, extrapolation, numerical integration, solution of linear and nonlinear equations. They should know the basic algorithms, their properties (convergence properties, complexity, conditioning), and they should be able to realize the algorithms in a modern computing environment.
Basic error concepts: condition of mathematical problems, data error, discretization error, round-off error. Numerical solution of linear and nonlinear systems of equations, numerical differentiation and integration, polynomial interpolation and approximation, numerical solution of differential equation
The lecture takes place every Tuesday 8:00 - 10:00 am online via Zoom. The link is available in TUWEL.
The algorithms are presented and analyzed mathematically with respect to their convergence and complexity properties. Numerical examples illustrate the algorithms' properties. The exercises deepen the understanding of the algorithms and their properties by some further mathematical analysis, implementation of the algorithms in Matlab or Python, and studies of numerical examples that showcase the behavior of the algorithms.
