Main content
This entry is from Winter semester 2022/23 and might be obsolete. You can find a current equivalent here.
Numerical Solution Methods for Finite Dimensional Problems
(dt. Numerik endlichdimensionaler Probleme)
Level, degree of commitment | Specialization 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(s): 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 the degree program M.Sc. Mathematics. |
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.
Applicability
Module imported from M.Sc. Mathematics.
It can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- B.Sc. Business Mathematics
- M.Sc. Data Science
- M.Sc. Computer Science
- M.Sc. Mathematics
- M.Sc. Business Mathematics
- LAaG Mathematics
When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.
The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.
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 Winter semester 2022/23. 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:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24
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.