## Applied Laplace Transforms and Z-Transforms for Scientists and Engineers: A Computational Approach Using a Mathematica PackageThe 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, especially for solving differential equations. What the Laplace transformation does in the field of differential equations, the z-transformation achieves for difference equations. The two theories are parallel and have many analogies. Laplace and z transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. This book does not use the operational calculus of Mikusinski, whose approach is based on abstract algebra and is not readily accessible to engineers and scientists. The symbolic computation capability of Mathematica can now be used in favor of the Laplace and z-transformations. The first version of the Mathematica Package LaplaceAndzTransforrns developed by the author appeared ten years ago. The Package computes not only Laplace and z-transforms but also includes many routines from various domains of applications. Upon loading the Package, about one hundred and fifty new commands are added to the built-in commands of Mathematica. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available. The Package substantially enhances the Laplace and z-transformation facilities of Mathematica. The book is mainly designed for readers working in the field of applications. |

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### Contents

zTransformation | 77 |

Laplace Transforms with the Package | 115 |

zTransformation with the Package | 153 |

Further Topics | 215 |

Further Topics | 287 |

Examples from Electricity | 321 |

Examples from Control Engineering | 351 |

### Other editions - View all

Applied Laplace Transforms and z-Transforms for Scientists and Engineers: A ... Urs Graf Limited preview - 2012 |

Applied Laplace Transforms and z-Transforms for Scientists and Engineers: A ... Urs Graf No preview available - 2011 |

Applied Laplace Transforms and z-Transforms for Scientists and Engineers: A ... Urs Graf No preview available - 2012 |

### Common terms and phrases

absolute convergence advanced z-transform applied assume asymptotic expansion asymptotically stable AxesLabel boundary condition boundary value problem bounded exponential growth branch point Chop Closing Contour Condition coefficients compute constant controller configuration convolution theorem correspondence Cos[t cosh defined difference equations differential equation differentiation rule Dirac Impulse discrete Laplace transform discrete signal example expression feedback given Green's function holomorphic image equation image function implies Infinity initial conditions initial value problem input integration contour inverse Laplace transform inverse z-transform Laplace image Laplace integral large values lemma linear Mathematica meromorphic function method numerical obtain original function original shift rule output Package parameter pendulum physicalvalues Plot PlotRange poles polynomial positive rational function rational image function real axis right half-plane right-hand side sampled-data satisfied Section sequence f(k shift rule solution Sqrt Sqrt[s Summation temperature transfer matrix two-sided Laplace transform unit-circle vector voltage yields zero