The Laplace Transform
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The Laplace Transform
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Author : Joel L. Schiff
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05
The Laplace Transform written by Joel L. Schiff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un dergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + · · · + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A. 6)? Or, in many proofs it is required to take the limit inside an integral. This is always fraught with danger, especially with an improper integral, and not always justified. I have given complete details (sometimes in the Appendix) whenever this procedure is required. IX X Preface Furthermore, it is sometimes desirable to take the Laplace trans form of an infinite series term by term. Again it is shown that this cannot always be done, and specific sufficient conditions are established to justify this operation.
The Laplace Transform
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Author : Richard Bellman
language : en
Publisher: World Scientific
Release Date : 1984-11-01
The Laplace Transform written by Richard Bellman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-11-01 with Laplace transformation categories.
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.
Laplace Transforms Essentials
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Author : Morteza Shafii-Mousavi
language : en
Publisher: Research & Education Assoc.
Release Date : 2013-01-01
Laplace Transforms Essentials written by Morteza Shafii-Mousavi and has been published by Research & Education Assoc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Laplace Transforms includes the Laplace transform, the inverse Laplace transform, special functions and properties, applications to ordinary linear differential equations, Fourier transforms, applications to integral and difference equations, applications to boundary value problems, and tables.
Introduction To The Laplace Transform
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Author : Peter K.F. Kuhfittig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Introduction To The Laplace Transform written by Peter K.F. Kuhfittig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Engineering Applications Of The Laplace Transform
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Author : Y.H. Gangadharaiah
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2021-08-25
Engineering Applications Of The Laplace Transform written by Y.H. Gangadharaiah and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-25 with Mathematics categories.
This book is devoted to one of the most critical areas of applied mathematics, namely the Laplace transform technique for linear time invariance systems arising from the fields of electrical and mechanical engineering. It focuses on introducing Laplace transformation and its operating properties, finding inverse Laplace transformation through different methods, and describing transfer function applications for mechanical and electrical networks to develop input and output relationships. It also discusses solutions of initial value problems, the state-variables approach, and the solution of boundary value problems connected with partial differential equations.
An Introduction To The Laplace Transform And The Z Transform
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Author : Anthony C. Grove
language : en
Publisher:
Release Date : 1991
An Introduction To The Laplace Transform And The Z Transform written by Anthony C. Grove and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
An Introduction To Complex Analysis And The Laplace Transform
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Author : Vladimir Eiderman
language : en
Publisher: CRC Press
Release Date : 2021-12-20
An Introduction To Complex Analysis And The Laplace Transform written by Vladimir Eiderman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-20 with Mathematics categories.
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.
The Laplace Transform
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Author : Earl David Rainville
language : en
Publisher:
Release Date : 1963
The Laplace Transform written by Earl David Rainville and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Laplace transformation categories.
Introductory Laplace Transform With Applications
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Author : Dalpatadu
language : en
Publisher: Trafford Publishing
Release Date : 2015-07-17
Introductory Laplace Transform With Applications written by Dalpatadu and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-17 with Mathematics categories.
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.
An Introduction To The Laplace Transformation
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Author : John Conrad Jaeger
language : en
Publisher:
Release Date : 1969
An Introduction To The Laplace Transformation written by John Conrad Jaeger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Integral transforms categories.