Introduction To The Theory And Application Of The Laplace Transformation
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Introduction To The Theory And Application Of The Laplace Transformation
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Author : Gustav Doetsch
language : en
Publisher: Springer
Release Date : 1974
Introduction To The Theory And Application Of The Laplace Transformation written by Gustav Doetsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Laplace transformation categories.
In anglo-american literature there exist numerous books, devoted to the application of the Laplace transformation in technical domains such as electrotechnics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified manner, presuming special properties with respect to the transformed func tions, which allow easy proofs. By contrast, the present book intends principally to develop those parts of the theory of the Laplace transformation, which are needed by mathematicians, physicists a,nd engineers in their daily routine work, but in complete generality and with detailed, exact proofs. The applications to other mathematical domains and to technical prob lems are inserted, when the theory is adequately· developed to present the tools necessary for their treatment. Since the book proceeds, not in a rigorously systematic manner, but rather from easier to more difficult topics, it is suited to be read from the beginning as a textbook, when one wishes to familiarize oneself for the first time with the Laplace transforma tion. For those who are interested only in particular details, all results are specified in "Theorems" with explicitly formulated assumptions and assertions. Chapters 1-14 treat the question of convergence and the mapping properties of the Laplace transformation. The interpretation of the transformation as the mapping of one function space to another (original and image functions) constitutes the dom inating idea of all subsequent considerations.
Introduction To The Theory And Application Of The Laplace Transformation
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Author : Gustav Doetsch
language : en
Publisher:
Release Date : 1970
Introduction To The Theory And Application Of The Laplace Transformation written by Gustav Doetsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Laplace transformation categories.
Introduction To The Theory And Application Of The Laplace Transformation
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Author : Gustav Doetsch
language : de
Publisher:
Release Date : 1974
Introduction To The Theory And Application Of The Laplace Transformation written by Gustav Doetsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Introduction To The Theory And Application Of The Laplace Transformation Translation By Walter Nader
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Author :
language : en
Publisher:
Release Date : 1941
Introduction To The Theory And Application Of The Laplace Transformation Translation By Walter Nader written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1941 with Laplace transformation categories.
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.
An Introduction To Transform Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1971-09-30
An Introduction To Transform Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-09-30 with Mathematics categories.
An introduction to transform theory
Laplace Transforms And Their Applications To Differential Equations
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Author : N.W. McLachlan
language : en
Publisher: Courier Corporation
Release Date : 2014-11-19
Laplace Transforms And Their Applications To Differential Equations written by N.W. McLachlan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This introduction to modern operational calculus offers a classic exposition of Laplace transform theory and its application to the solution of ordinary and partial differential equations. The treatment is addressed to graduate students in engineering, physics, and applied mathematics and may be used as a primary text or supplementary reading. Chief topics include the theorems or rules of the operational calculus, evaluation of integrals and establishment of mathematical relationships, derivation of Laplace transforms of various functions, the Laplace transform for a finite interval, and other subjects. Many problems and illustrative examples appear throughout the book, which is further augmented by helpful Appendixes. Dover (2014) republication of the 1962 (Dover) revised edition of Modern Operational Calculus with Applications in Technical Mathematics, Macmillan, London, 1948. See every Dover book in print at www.doverpublications.com
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.
Introduction To The Theory And Application Of The Laplace Transformation
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Author : G. Doetsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To The Theory And Application Of The Laplace Transformation written by G. Doetsch 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 2012-12-06 with Mathematics categories.
In anglo-american literature there exist numerous books, devoted to the application of the Laplace transformation in technical domains such as electrotechnics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified manner, presuming special properties with respect to the transformed func tions, which allow easy proofs. By contrast, the present book intends principally to develop those parts of the theory of the Laplace transformation, which are needed by mathematicians, physicists a,nd engineers in their daily routine work, but in complete generality and with detailed, exact proofs. The applications to other mathematical domains and to technical prob lems are inserted, when the theory is adequately· developed to present the tools necessary for their treatment. Since the book proceeds, not in a rigorously systematic manner, but rather from easier to more difficult topics, it is suited to be read from the beginning as a textbook, when one wishes to familiarize oneself for the first time with the Laplace transforma tion. For those who are interested only in particular details, all results are specified in "Theorems" with explicitly formulated assumptions and assertions. Chapters 1-14 treat the question of convergence and the mapping properties of the Laplace transformation. The interpretation of the transformation as the mapping of one function space to another (original and image functions) constitutes the dom inating idea of all subsequent considerations.
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.