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German original

Numerical Analysis
(dt. Numerik (Numerische Basisverfahren))

Level, degree of commitment in original study programme Intermediate module, required module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Mathematics.
Original study programme B.Sc. Mathematik / Mathematik Aufbaumodule (Kernfächer)
Duration,
frequency
One semester,
each summer semester
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

Fundamentals of computer arithmetic and measures for error control. Basic methods for the solution of linear and nonlinear systems of equations, in particular also compensation problems. Methods for the representation and approximation of functions.


Qualification Goals

The students shall

  • Develop understanding of the basic principles of numerics and confidently master basic numerical methods for important mathematical problems in theory and practice,
  • Develop insight into the practical solution of mathematical problems and sensitivity for special numerical problems such as faulty arithmetic and error control,
  • be able to apply numerical methods competently. In particular, the numerical methods are to be converted into efficient software and the appropriate selection of existing standard software is to be trained,
  • to recognize the many cross connections to other areas such as linear algebra, analysis, geometry, etc. and acquire basic knowledge for in-depth numerics modules,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstract ability, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.


Recommended Reading

  • Stoer/Bulirsch: Numerische Mathematik I, Springer Verlag 2007;
  • Deuflhard/Hohmann: Numerische Mathematik I, de Gruyter 2002;
  • Hanke-Bourgeois, M.: Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens, Teubner, 2002.



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.