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On The 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 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 Heaviside's Operational Calculus Made Easy by : T. H. Turney
Download or read book Heaviside's Operational Calculus Made Easy written by T. H. Turney and published by Goldberg Press. This book was released on 2010-11 with total page 106 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 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 Introduction to the Operational Calculus by : Lothar Berg
Download or read book Introduction to the Operational Calculus written by Lothar Berg and published by . This book was released on 1967 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complements of Higher Mathematics by : Marin Marin
Download or read book Complements of Higher Mathematics written by Marin Marin and published by Springer. This book was released on 2018-02-13 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the remarkable importance of special functions, operational calculus, and variational methods. A considerable portion of the book is dedicated to second-order partial differential equations, as they offer mathematical models of various phenomena in physics and engineering. The book provides students and researchers with essential help on key mathematical topics, which are applied to a range of practical problems. These topics were chosen because, after teaching university courses for many years, the authors have found them to be essential, especially in the contexts of technology, engineering and economics. Given the diversity topics included in the book, the presentation of each is limited to the basic notions and results of the respective mathematical domain. Chapter 1 is devoted to complex functions. Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding of the role that the theory of functions of a complex variable plays in mathematical physics, especially in the modeling of plane problems. In addition, the book demonstrates the importance of the theories of special functions, operational calculus, and variational calculus. In the last chapter, the authors discuss the basic elements of one of the most modern areas of mathematics, namely the theory of optimal control.
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 Essentials of Partial Differential Equations by : Marin Marin
Download or read book Essentials of Partial Differential Equations written by Marin Marin and published by Springer. This book was released on 2018-05-09 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject. Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations.
Download or read book Oliver Heaviside written by Paul J. Nahin and published by JHU Press. This book was released on 2002-11-13 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acclaimed biography of the pioneer of modern electrical theory featuring a new preface by author. "He was a man who often was incapable of conducting himself properly in the most elementary social interactions. His only continuing contacts with women were limited to his mother, nieces, and housekeepers. He was a man who knew the power of money and desired it, but refused to work for it, preferring to live off the sweat of his family and long-suffering friends, whom he often insulted even as they paid his bills."—Excerpt from the book This, then, was Oliver Heaviside, a pioneer of modern electrical theory. Born into a low social class of Victorian England, Heaviside made advances in mathematics by introducing the operational calculus; in physics, where he formulated the modern-day expressions of Maxwell's Laws of electromagnetism; and in electrical engineering, through his duplex equations. With a new preface by the author, this acclaimed biography will appeal to historians of technology and science, as well as to scientists and engineers who wish to learn more about this remarkable man.
Book Synopsis The Forgotten Genius of Oliver Heaviside by : Basil Mahon
Download or read book The Forgotten Genius of Oliver Heaviside written by Basil Mahon and published by Prometheus Books. This book was released on 2017 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This biography of Oliver Heaviside profiles the life of an underappreciated genius and describes his many contributions to electrical science, which proved to be essential to the future of mass communications"--
Book Synopsis Electromagnetic Theory by : Oliver Heaviside
Download or read book Electromagnetic Theory written by Oliver Heaviside and published by . This book was released on 1893 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operational Methods by : V. P. Maslov
Download or read book Operational Methods written by V. P. Maslov and published by . This book was released on 1976 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis Fractional Calculus in Bioengineering by : Richard L. Magin
Download or read book Fractional Calculus in Bioengineering written by Richard L. Magin and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is written for bioengineers who wish to learn more about fractional calculus (integration and differentiation of arbitrary order) and the ways in which it can be used to solve biomedical problems. However, the text covers a wide range of topics (bioelectrodes, biomaterials, neural networks, etc.) that I hope will be of interest to other scientists and engineers as well as to bioengineers. Examples and exercises show that with only a small change in notation and perspective, fractional calculus extends many of the modeling capabilities of conventional calculus and integer order differential equations. By combining an "engineer's" approach to fractional calculus - largely through using the Laplace transform - with examples taken from a variety of biomedical applications, this book will help new students learn to use the techniques of fractional calculus. The second edition of this book contains updates and corrections to equations and descriptions from the first edition"--
Book Synopsis The Mathematics of Diffusion by : John Crank
Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Book Synopsis Hypernumbers and Extrafunctions by : Mark Burgin
Download or read book Hypernumbers and Extrafunctions written by Mark Burgin and published by Springer Science & Business Media. This book was released on 2012-05-16 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.
