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, QR-decomposition and SVD, FFT, numerical solution of differential equation
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.
Checkmark exercise and two tests
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There will be lecture notes in TUWEL!
linear algebra and analysis. Matlab or Python
