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Heaviside Operational Calculus
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Book Synopsis Operational Calculus by : Kosaku Yosida
Download or read book Operational Calculus written by Kosaku Yosida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Heaviside's Operational Calculus Made Easy by : Thomas Henry Turney
Download or read book Heaviside's Operational Calculus Made Easy written by Thomas Henry Turney and published by . This book was released on 1946 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heaviside Operational Calculus by : Kurt Otto Friedrichs
Download or read book Heaviside Operational Calculus written by Kurt Otto Friedrichs and published by . This book was released on 1948 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heaviside Operational Calculus by : Douglas H. Moore
Download or read book Heaviside Operational Calculus written by Douglas H. Moore and published by . This book was released on 1971 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Heaviside Operational Calculus by : Albert Huntoon Wait
Download or read book On the Heaviside Operational Calculus written by Albert Huntoon Wait and published by . This book was released on 1926 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operational Calculus by : Iosyp Zakharovych Shtokalo
Download or read book Operational Calculus written by Iosyp Zakharovych Shtokalo and published by . This book was released on 1976 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operational Calculus and Related Topics by : A. P. Prudnikov
Download or read book Operational Calculus and Related Topics written by A. P. Prudnikov and published by CRC Press. This book was released on 2006-08-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Operational Calculus by : Jan Mikusinski
Download or read book Operational Calculus written by Jan Mikusinski and published by Elsevier. This book was released on 2014-07-14 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operational Calculus and Generalized Functions by : Arthur Erdelyi
Download or read book Operational Calculus and Generalized Functions written by Arthur Erdelyi and published by Courier Corporation. This book was released on 2013-07-24 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operational Calculus by : Gregors Krabbe
Download or read book Operational Calculus written by Gregors Krabbe and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Introduction To The Operational Calculus by : Lothar Berg
Download or read book Introduction To The Operational Calculus written by Lothar Berg and published by Elsevier. This book was released on 2013-07-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operational Calculus by : Kosaku Yosida
Download or read book Operational Calculus written by Kosaku Yosida and published by Springer. This book was released on 1984-07-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Heaviside Operational Calculus by : Douglas H. Moore
Download or read book Heaviside Operational Calculus written by Douglas H. Moore and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Electric Circuit Theory and the Operational Calculus by : John Renshaw Carson
Download or read book Electric Circuit Theory and the Operational Calculus written by John Renshaw Carson and published by . This book was released on 1926 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heaviside's Operational Calculus as Applied to Engineering and Physics by : Ernst Julius Berg
Download or read book Heaviside's Operational Calculus as Applied to Engineering and Physics written by Ernst Julius Berg and published by . This book was released on 1936 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Heaviside Operational Calculus by : Jeremy Staines
Download or read book The Heaviside Operational Calculus written by Jeremy Staines and published by . This book was released on 2013-08-09 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the little-known part of the mathematical history of what we nowadays call the Laplace Transform method of solving differential equations. It is a purely mathematical development of Heaviside's operational methods of electric circuit analysis which requires of the reader a basic knowledge of differential equations, electric circuit theory, Laplace transforms, and some vector analysis, as applied to electromagnetic theory.
Book Synopsis Operational Calculus by : Thomas K. Boehme
Download or read book Operational Calculus written by Thomas K. Boehme and published by Elsevier. This book was released on 2014-08-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
