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.