mat996 - Introduction to Numerical Analysis (Complete module description)
Module label | Introduction to Numerical Analysis |
Module code | mat996 |
Credit points | 6.0 KP |
Workload | 180 h |
Institute directory | Department of Mathematics |
Applicability of the module |
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Prerequisites | Analysis I, Lineare Algebra |
Skills to be acquired in this module | 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 |
Module contents | · 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 |
Recommended reading | 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. |
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Language of instruction | German |
Duration (semesters) | 1 Semester |
Module frequency | every year |
Module capacity | unlimited |
Reference text | Als 6 KP Modul werden Vorlesung und Übungen nur in den ersten 2/3 des Semesters besucht. |
Type of course | Comment | SWS | Frequency | Workload of compulsory attendance |
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Lecture | 2.7 | WiSe | 37 | |
Exercises | 1.3 | WiSe | 19 | |
Total module attendance time | 56 h |
Examination | Prüfungszeiten | Type of examination |
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Final exam of module | At the end of the lecture period written exam |
Final exam of module |