Applied Laplace Transforms and z-Transforms for Scientists and Engineers

This book presents theory and applications of Laplace and z-transforms together with a Mathematica package developed by the author. The package substantially enhances the bulit-in facilities of Mathematica. The emphasis lies on the computational and applied side, particularly in the fields of control engineering, electrical engineering, and mechanics. Many worked out examples from engineering and sciences illustrate the applicability of the theory and the usage of the package. Students, instructors, practical engineers and researchers working in the field of control, electricity or mechanics will find this textbook a most valuable resource and will profit from the package and further examples and Mathematica notebooks on the included CD-ROM.

Clear introduction to Laplace- and z-transforms together with some advanced subjects related to applications A Mathematica package for computing Laplace- and z-transforms, including numerical inversion of Laplace transforms Textbook and work-book for applications in the field of control, electrical and mechanical engineering Accompanying CD contains the software package and many examples Includes supplementary material: sn.pub/extras

Inhalt
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.

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