An Introduction To The Operational Calculus
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Introduction To The Operational Calculus
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Author : Lothar Berg
language : en
Publisher: Elsevier
Release Date : 2013-07-19
Introduction To The Operational Calculus written by Lothar Berg and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.
Introduction to the Operational Calculus is a translation of "Einfuhrung in die Operatorenrechnung, Second Edition." This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work "Operational Calculus." Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant coefficients. In using operational calculus to solve more complicated problems than those of ordinary differential equations with constant coefficients, the concept of convergence assumes a significant role in the field of operators. This book also extends the Laplace transformation and applies it to non-transformable functions. This text also present three methods in which operational calculus can be modified and become useful in solving specific ranges of problems. These methods pertain to the finite Laplace transformation, to partial differential equations, and to the Volterra integral equations and ordinary differential equations with variable coefficients. This book can prove valuable for mathematicians, students, and professor of calculus and advanced mathematics.
An Introduction To The Operational Calculus
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Author : Walter J. Seeley
language : en
Publisher:
Release Date : 1942
An Introduction To The Operational Calculus written by Walter J. Seeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1942 with categories.
Operational Calculus And Related Topics
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Author : A. P. Prudnikov
language : en
Publisher: CRC Press
Release Date : 2006-08-15
Operational Calculus And Related Topics written by A. P. Prudnikov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-15 with Mathematics categories.
Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering. Operational Calculus and Related Topics highlights the classical methods and applications as well as the recent advan
Operational Calculus
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Author : Kosaku Yosida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Operational Calculus written by Kosaku Yosida 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 the end of the last century, Oliver Heaviside inaugurated an operational calculus in connection with his researches in electromagnetic theory. In his operational calculus, the operator of differentiation was denoted by the symbol "p". The explanation of this operator p as given by him was difficult to understand and to use, and the range of the valid ity of his calculus remains unclear still now, although it was widely noticed that his calculus gives correct results in general. In the 1930s, Gustav Doetsch and many other mathematicians began to strive for the mathematical foundation of Heaviside's operational calculus by virtue of the Laplace transform -pt e f(t)dt. ( However, the use of such integrals naturally confronts restrictions con cerning the growth behavior of the numerical function f(t) as t ~ ~. At about the midcentury, Jan Mikusinski invented the theory of con volution quotients, based upon the Titchmarsh convolution theorem: If f(t) and get) are continuous functions defined on [O,~) such that the convolution f~ f(t-u)g(u)du =0, then either f(t) =0 or get) =0 must hold. The convolution quotients include the operator of differentiation "s" and related operators. Mikusinski's operational calculus gives a satisfactory basis of Heaviside's operational calculus; it can be applied successfully to linear ordinary differential equations with constant coefficients as well as to the telegraph equation which includes both the wave and heat equa tions with constant coefficients.
An Introduction To The Operational Calculus By Walter J Seeley
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Author : Walter James Seeley
language : en
Publisher:
Release Date :
An Introduction To The Operational Calculus By Walter J Seeley written by Walter James Seeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Calculus, Operational categories.
An Introduction To The Operational Calculus 2nd Impr
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Author : W.J. Seeley
language : en
Publisher:
Release Date : 1941
An Introduction To The Operational Calculus 2nd Impr written by W.J. Seeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1941 with categories.
Feynman S Operational Calculus And Beyond
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Author : Gerald W Johnson
language : en
Publisher: OUP Oxford
Release Date : 2015-08-06
Feynman S Operational Calculus And Beyond written by Gerald W Johnson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-06 with Science categories.
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.
An Introduction To The Operational Calculus
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Author : Walter James Seeley
language : en
Publisher:
Release Date : 1941
An Introduction To The Operational Calculus written by Walter James Seeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1941 with Calculus, Operational categories.
Operational Calculus And Generalized Functions
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Author : Arthur Erdelyi
language : en
Publisher: Courier Corporation
Release Date : 2013-07-24
Operational Calculus And Generalized Functions written by Arthur Erdelyi and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-24 with Mathematics categories.
Suitable for advanced undergraduates and graduate students, this brief monograph examines elementary and convergence theories of convolution quotients, differential equations involving operator functions, exponential functions of operators. Solutions. 1962 edition.
Introduction To The Operational Calculus
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Author : Hermann Vinterberg
language : en
Publisher:
Release Date : 1967
Introduction To The Operational Calculus written by Hermann Vinterberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.