mat996 - Introduction to Numerical Analysis (Complete module description)

Analysis I, Lineare Algebra

The students learn and analyze the basic numerical methods. The students learn to implement the basic numerical methods in a computer program.


Professional competence
The students:
· learn basic numerical methods and algorithms
· analyze properties of the numerical methods using rigorous mathematical tools
· implement the basic numerical methods in a computer program
· interpret results of computer simulations

Methodological competence
The students:
· analyze algorithms with mathematical tools
· implement numerical algorithms for concrete problems

Social competence
The students:
· develop solutions to given problems in groups
· accept constructive criticism

Personal competence
The students:
· reflect their solution strategies
· deepen their understanding of the presented mathematical and algorithmical concepts with exercises and adopt the solution methods

· Numerical methods for linear systems: LU-, Cholesky decompositions, iterative methods
· Numerical methods for nonlinear equations: fix-point iterations, Netwon's Method
· Polynomials, spline and trigonometric interpolation
· Numerical integration: Newton-Cotes, Gauss quadrature rules, adaptive quadrature and extrapolation methods
· Stability and conditioning of algorithms and problems

R. Plato: Numerische Mathematik kompakt, Vieweg + Teubner, 2010.
Stoer, Bulirsch: Numerische Mathematik 1 und 2, Springer, 2007, 2005.
P. Deuflhard, A. Hohmann: Numerische Mathematik 1, de Gruyter, 2008.
H.R. Schwarz, N. Köckler: Numerische Mathematik, Vieweg+Teubner, 2008.
M. Hanke-Bourgeois: Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens, Vieweg+Teubner, 2008.

Als 6 KP Modul werden Vorlesung und Übungen nur in den ersten 2/3 des Semesters besucht.

At the end of the lecture period written exam

Final exam of module