mat996 - Introduction to Numerical Analysis (Complete module description)

mat996 - Introduction to Numerical Analysis (Complete module description)

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Module label Introduction to Numerical Analysis
Modulkürzel mat996
Credit points 6.0 KP
Workload 180 h
Institute directory Department of Mathematics
Verwendbarkeit des Moduls
  • Bachelor's Programme Business Informatics (Bachelor) >
  • Bachelor's Programme Computing Science (Bachelor) >
  • Master's Programme Computing Science (Master) >
Zuständige Personen
  • Chernov, Alexey (module responsibility)
  • Schöpfer, Frank (module responsibility)
Prerequisites
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
Literaturempfehlungen
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
Form of instruction Comment SWS Frequency Workload of compulsory attendance
Lecture 2.7 WiSe 37
Exercises 1.3 WiSe 19
Präsenzzeit Modul insgesamt 56 h
Examination Prüfungszeiten Type of examination
Final exam of module
At the end of the lecture period written exam
Final exam of module