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Numerical Methods
Numerische Methoden
Last Updated: 2026-02-05 14:57:28
Abstract
The course introduces numerical methods according to the type of problemthey tackle. The tutorial will include both theoretical exercises andpractical tasks. The latter will mainly employ on the numerical programming languageMATLAB, some will have to be done in C.Prerequisite is familiarity with basic calculus and linear algebra.
Objective
This course intends to introduce to fundamental numerical methods that form the foundation of numerical simulation in engineering science. Participants should learn about classes of methods, should understand their principles and will be taught how to assess, implement, and apply them. During the course they will become familiar with basic techniques and concepts of numerical analysis. They should be enabled to select and adapt suitable numerical methods for a particular problem.
Content
1. Numerical linear algebra 1.1. Matrix decompositions and solution of linear systems of equations 1.2. Linear least squares problems 1.3. Eigenvalue problems 1.4. Singular value decompositions 1.5. Sparse matrix techniques 2. Numerical transformations 2.1. Fast Fourier transform (FFT) 2.2. Wavelet transforms 2.3. Numerical integral transforms 4. Numerical solution of elliptic boundary value problems 4.1. Finite element methods (FEM) 4.2. Finite volume methods 4.3. Finite difference methods 4.4. Spectral methods 3. Numerical methods for ordinary differential equations 3.1. Single step methods 3.2. Methods for stiff ODEs 3.3. Geometric numerical integration 3.4. Collocation schemes for 2-point boundary value problems 5. Iterative schemes for systems of equations 5.1. Fixed point interation 5.2. Linear iterations for linear systems of equations 5.3. Conjugate gradients (CG) and Krylov subspace methods 5.4. Newton's method and quasi Newton methods
Resources
Lecture Notes
Kein Skript
Literature
M. Hanke Bourgeois: Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens, BG Teubner, Stuttgart, 2002 P. Deuflhard, A. Hohmann: Numerische Mathematik I. Eine algorithmisch orientierte Einfuehrung (3. Auflage), W deGruyter, Berlin, 2002 P. Deuflhard, F. Bornemann: Numerische Mathematik II. Gewoehnliche Differentialgleichungen (2. Auflage). W DeGruyter, Berlin 2002 Numerical recipes: http://www.nr.com/
General Information
- Language
- German
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 105 minutes
- Aids
- 20 Seiten selbstgeschriebener Notizen, keine Kopien, nichtvernetzter Taschenrechner.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Numerische Methoden |
|
2 h weekly |
| exercise | Numerische Methoden |
|
1 h weekly |