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German original

Numerical Solution Methods for Finite Dimensional Problems
(dt. Numerik endlichdimensionaler Probleme)

Level, degree of commitment in original study programme Advanced module, compulsory elective 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 M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency		 One semester,
Jedes zweite Wintersemester
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

Methods for eigenvalue problems of matrices, fast iteration methods for large systems of equations. Selected additions, such as curve tracking for nonlinear equation systems or fast decomposition methods (FFT, wavelet transformation)


Qualification Goals

The students shall

  • be empowered to classify practical problems in relation to applicable methods and the effort involved,
  • deal with different methods, their different applications and the differences in efficiency and universality of the methods,
  • see how to build up and analyze solution methods from different basic methods for complex tasks,
  • learn about the development of efficient methods by combining building blocks of different characteristics in the core topic of iterative methods for large systems of equations,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the abstraction capability, 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 Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Numerical Analysis.


Recommended Reading

  • Stoer, J., Bulirsch, R.: Numerische Mathematik II, Springer, 2000;
  • Golub, G., van Loan, C.: Matrix Computations, The Johns Hopkins University Press, 1990;
  • 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 Wintersemester 2021/22. 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.