Applied Laplace Transforms and z-Transforms for Scientists and Engineers A Computational Approach using a Mathematica Package
The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. Laplace transformation methods provide easy and effective techniques for solving many problems arising in various fields of science and engineering, especia...
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| Format: | eBook |
| Language: | English |
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Basel
Birkhäuser
2004, 2004
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| Edition: | 1st ed. 2004 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Laplace Transformation
- 1.1 The One-Sided Laplace Transform
- 1.2 The Two-Sided Laplace Transform
- 1.3 Ordinary Linear Differential Equations
- 2 z-Transformation
- 2.1 z-Transforms and Inverse z-Transforms
- 2.2 Difference Equations
- 3 Laplace Transforms with the Package
- 3.1 Basics
- 3.2 The Use of Transformation Rules
- 3.3 The Finite Laplace Transform
- 3.4 Special Functions
- 3.5 Inverse Laplace Transformation
- 3.6 Differential Equations
- 4 z-Transformation with the Package
- 4.1 Basics
- 4.2 Use of Transformation Rules
- 4.3 Difference Equations
- 5 Applications To Automatic Control
- 5.1 Controller Configurations
- 5.2 State-Variable Analysis
- 5.3 Second Order Differential Systems
- 5.4 Stability
- 5.5 Frequency Analysis
- 5.6 Sampled-Data Control Systems
- 6 Laplace Transformation: Further Topics
- 6.1 The Complex Inversion Formula
- 6.2 Laplace Transforms and Asymptotics
- 6.3 Differential Equations
- 7 z-Transformation: Further Topics
- 7.1 The Advanced z-Transformation
- 7.2 Applications
- 7.3 Use of the Package
- 8 Examples from Electricity
- 8.1 Transmission Lines
- 8.2 Electrical Networks
- 9 Examples from Control Engineering
- 9.1 Control of an Inverted Pendulum
- 9.2 Controling a Seesaw-Pendulum
- 9.3 Control of a DC Motor
- 9.4 A Magnetic-Ball-Suspension-System
- 9.5 A Sampled-Data State-Variable Control System
- 10 Heat Conduction and Vibration Problems
- 10.1 Flow of Heat
- 10.2 Waves and Vibrations in Elastic Solids
- 11 Further Techniques
- 11.1 Duhamel’s Formulas
- 11.2 Green’s Functions
- 11.3 Fundamental Solutions
- 11.4 Finite Fourier Transforms
- 12 Numerical Inversion of Laplace Transforms
- 12.1 Inversion by the Use of Laguerre Functions
- 12.2 Inversion by Use of Fourier Analysis
- 12.3 The Use of Gaussian Quadrature Formulas
- 12.4 The Method of Gaver and Stehfest
- 12.5 Example
- Appendix: Package Commands