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	Bachelor's Programme Business Informatics (Bachelor) > Aufbaucurriculum-Wahlbereich Mathematik Bachelor's Programme Computing Science (Bachelor) > Wahlpflichtbereich Mathematik Master's Programme Computing Science (Master) > Module aus anderen Studiengängen
Responsible persons	Chernov, Alexey (module responsibility) Schöpfer, Frank (module responsibility)
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.
Links
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 module	Wahlpflicht / Elective
Module level	AC (Aufbaucurriculum / Composition)
Teaching/Learning method	Vorlesung + Übung

Type of course	SWS	Frequency	Workload of compulsory attendance
Lecture	2.7	WiSe	37
Exercises	1.3	WiSe	19
Total module attendance time			56 h

Examination	Prüfungszeiten	Type of examination
Final exam of module	At the end of the lecture period written exam	Final exam of module