Operational Calculus
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Operational Calculus
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Author : Jan Mikusinski
language : en
Publisher: Elsevier
Release Date : 2014-07-14
Operational Calculus written by Jan Mikusinski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Pure and Applied Mathematics, Volume 109: Operational Calculus, Second Edition. Volume I presents the foundations of operational calculus and its applications to physics and engineering. This book introduces the operators algebraically as a kind of fractions. Organized into three parts, this volume begins with an overview of the concept as well as the characteristics of a convolution of continuous functions. This text then examines the transitivity, associativity, and distributivity of convolution with regard to addition. Other parts consider the methods of solving other difference equations, particularly in the field of electrical engineering, in which the variable runs over integer values only. This book discusses as well the solution of differential equations under given initial conditions. The final part deals with the characteristic properties of a derivative and provides the definition of algebraic derivative to any operators. This book is a valuable resource for physicists, electrical engineers, mathematicians, and research workers.
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.
Operational Calculus
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Author : Iosyp Zakharovych Shtokalo
language : en
Publisher:
Release Date : 1976
Operational Calculus written by Iosyp Zakharovych Shtokalo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Calculus, Operational categories.
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.
Operational Calculus
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Author : Thomas K. Boehme
language : en
Publisher: Elsevier
Release Date : 2014-08-01
Operational Calculus written by Thomas K. Boehme and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included. Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-homogeneous equations and applications of operational calculus to partial differential equations. The section section deals with the integral of an operational function and its applications, along with integral transformations. A definition of operators in terms of abstract algebra is then presented. Operators as generalized functions, power series of operators, and Laplace transform are also discussed. Formulas of the operational calculus and tables of functions round out the book. This monograph will be useful to engineers, who regard the operational calculus merely as a tool in their work, and readers who are interested in proofs of theorems and mathematical problems.
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 In Two Variables And Its Applications
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Author : V.A. Ditkin
language : en
Publisher: Courier Dover Publications
Release Date : 2017-09-13
Operational Calculus In Two Variables And Its Applications written by V.A. Ditkin and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-13 with Mathematics categories.
Concise treatment of fundamental theory explores two-dimensional Laplace transform and basic definitions, theorems, applications of operational calculus in two variables. Includes tables of formulae for various categories of functions. 1962 edition.
Operational Calculus
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Author : Gregors Krabbe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Operational Calculus written by Gregors Krabbe 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 2013-12-01 with Mathematics categories.
Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable sub stitute for HEAVISIDE's operational calculus*. However, the Laplace transform procedure is unsatisfactory from several viewpoints (some of these will be mentioned in this preface); the most obvious defect: the procedure cannot be applied to functions of rapid growth (such as the 2 function tr-+-exp(t)). In 1949 JAN MIKUSINSKI indicated how the un necessary restrictions required by the Laplace transform can be avoided by a direct approach, thereby gaining in notational as well as conceptual simplicity; this approach is carefully described in MIKUSINSKI's textbook "Operational Calculus" [M 1]. The aims of the present book are the same as MIKUSINSKI's [M 1]: a direct approach requiring no un-necessary restrictions. The present operational calculus is essentially equivalent to the "calcul symbolique" of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook "Theorie des distributions" by LAURENT SCHWARTZ).
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.
Operational Calculus
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Author : Jan Mikusiński
language : en
Publisher: Pergamon
Release Date : 1983
Operational Calculus written by Jan Mikusiński and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Calculus, Operational categories.