# Applied Laplace Transforms and z-Transforms for Scientists and Engineers

## A Computational Approach using a Mathematica Package

• Urs Graf
Textbook

1. Front Matter
Pages i-x
2. Urs Graf
Pages 1-76
3. Urs Graf
Pages 77-113
4. Urs Graf
Pages 115-152
5. Urs Graf
Pages 153-163
6. Urs Graf
Pages 165-213
7. Urs Graf
Pages 215-286
8. Urs Graf
Pages 287-319
9. Urs Graf
Pages 321-349
10. Urs Graf
Pages 351-390
11. Urs Graf
Pages 391-421
12. Urs Graf
Pages 423-465
13. Urs Graf
Pages 467-481
14. Urs Graf
Pages E1-E1
15. Back Matter
Pages 483-500

### Introduction

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, 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.

### Keywords

Fourier transform Mathematica calculus difference equation fourier analysis networks

#### Authors and affiliations

• Urs Graf
• 1
1. 1.Biel School of Engineering and ArchitectureBerne University of Applied SciencesBienneSwitzerland

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-0348-7846-3
• Copyright Information Springer Basel AG 2004
• Publisher Name Birkhäuser, Basel
• eBook Packages
• Print ISBN 978-3-7643-2427-8
• Online ISBN 978-3-0348-7846-3
• Buy this book on publisher's site
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