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Author : Anthony C. Grove
Publisher : Unknown
Page : 144 pages
File Size : 52,5 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015024770987
Author : Urs Graf
Publisher : Birkhäuser
Page : 501 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878463
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.
Author : Anonim
Publisher : Cambridge University Press
Page : 468 pages
File Size : 43,7 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521534410
This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.
Author : Peter K.F. Kuhfittig
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 51,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489922014
The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily. The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.
Author : Refaat El Attar
Publisher : Lulu.com
Page : 86 pages
File Size : 45,7 Mb
Release : 2006-07-01
Category : Technology & Engineering
ISBN : 9781411619791
Z-Transform is one of several transforms that are essential ? mathematical tools used in engineering and applied sciences. This ? short edition of this note is written to provide an introduction to the ? subject of Z-Transform. The material presented in this note can be ? covered in four to five 2-hour classroom lectures. Basic knowledge of ? calculus is needed. The note is not intended as a substitute for a text ? book on the subject. It is intended to help readers and students in ? engineering, mathematics and applied sciences understand the basic properties of Z-? Transform and some of the methods and techniques based on this ? transform to solve some engineering and science problems.? I have collected many examples and problems on the subject ? that might help the reader getting on-hand experience with the ? techniques presented in this note.?
Author : Robert Vich
Publisher : Springer
Page : 264 pages
File Size : 49,6 Mb
Release : 1987-06-30
Category : Mathematics
ISBN : 9027719179
Author : Daniel Fleisch
Publisher : Cambridge University Press
Page : 221 pages
File Size : 47,9 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9781009098496
Clear explanations and supportive online material develop an intuitive understanding of the meaning and use of Laplace.
Author : Vladimir Eiderman
Publisher : CRC Press
Page : 383 pages
File Size : 50,7 Mb
Release : 2021-12-20
Category : Mathematics
ISBN : 9781000511123
The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book. This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses. In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well. A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms. Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering.
Author : P.P.G. Dyke
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105053
This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Author : John Conrad Jaeger,Gordon Newstead
Publisher : Unknown
Page : 168 pages
File Size : 42,5 Mb
Release : 1969
Category : Integral transforms
ISBN : UOM:39015017335822
Author : Dalpatadu,Singh
Publisher : Trafford Publishing
Page : 185 pages
File Size : 44,8 Mb
Release : 2015-07-17
Category : Mathematics
ISBN : 9781490760698
One of the first applications of the modern Laplace transform was by Bateman in 1910 who used it to transform Rutherfords equations in his work on radioactive decay. The modeling of complex engineering and physical problems by linear differential equations has made the Laplace transform an indispensable mathematical tool for engineers and scientists. The method of Laplace transform for solving linear differential equations is very popular in the disciplines of electrical engineering, environmental engineering, hydrology, and petroleum engineering. This book presents some applications of Laplace transforms in these disciplines. Algorithms for the numerical inversion of Laplace transform are given, and a computer program in R for the Stehfest algorithm is included.
Author : Gustav Doetsch
Publisher : Van Nostrand Reinhold Company
Page : 266 pages
File Size : 40,6 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015000453236
Author : Paul B. Guest
Publisher : Unknown
Page : 424 pages
File Size : 46,8 Mb
Release : 1991
Category : Laplace transformation
ISBN : UOM:39015028908831
Author : Eliahu Ibrahim Jury
Publisher : Unknown
Page : 354 pages
File Size : 43,8 Mb
Release : 1964
Category : Mathematics
ISBN : UOM:39015000478076
Author : Earl David Rainville
Publisher : Unknown
Page : 124 pages
File Size : 41,7 Mb
Release : 1963
Category : Laplace transformation
ISBN : STANFORD:36105021399410