Institute of Engineering and Computational Mechanics | Universität Stuttgart

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University of Stuttgart

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	Institute of Engineering and Computational Mechanics
	Numerical Methods for Analysis and Optimization of Mechanical Systems

Informations to the Lecture Numerical Methods for Analysis and Optimization of Mechanical Systems:

Summerterm
Dr.-Ing. Pascal Ziegler
Prof. Dr.-Ing. Prof. E.h. Peter Eberhard

1. Introduction
2. General principles of numerical calculations

2.1 Definitions
2.2 Numerical principals
2.3 Machine numbers
2.4 Error estimation

3. Systems of linear algebraic equations

3.1 Motivation
3.2 Direct methods for square coefficient matrix
3.3 Cholesky-decomposition
3.4 Gauss-elimination
3.5 LR-decomposition
3.6 QR-decomposition
3.7 Iterative methodes for square coefficient matrix
3.8 Determinant of a matrix
3.9 Matrix inversion
3.10 Least square problem
3.11 Tools and numerical libraries for linear algebraic equations

4. Eigenvalue problems

4.1 General basics
4.2 Normal forms
4.3 Power methods
4.4 QR-algorithm
4.5 Calculation of eigenvectors
4.6 Practical solution of eigenvalue problems
4.7 Tools and numerical libraries for eigenvalue problems

5. Initial value problem for ordinary differantial equations

5.1 Motivation
5.2 Basic remarks>
5.3 Single-step methods
5.4 Extrapolation methods
5.5 Multistep methods
5.6 Comparison of the different methods
5.7 Tools and numerical libraries for initial value problems