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| Author | : R. G. Buschman |
| Publisher | : |
| Total Pages | : 256 |
| Release | : 2014-09-01 |
| Genre | : |
| ISBN | : 9781461312840 |
| Author | : Arthur Erdelyi |
| Publisher | : Courier Corporation |
| Total Pages | : 114 |
| Release | : 2013-07-17 |
| Genre | : Mathematics |
| ISBN | : 0486497127 |
"Based on a math course for advanced undergraduates and graduate students at Cal Tech, this brief monograph requires a background in advanced calculus. Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, exponential functions of operators, and problems in partial differential equations. Includes solutions. 1962 edition"--
| Author | : Ram Shankar Pathak |
| Publisher | : Routledge |
| Total Pages | : 432 |
| Release | : 2017-07-05 |
| Genre | : History |
| ISBN | : 135156269X |
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.
| Author | : Brychkov |
| Publisher | : CRC Press |
| Total Pages | : 362 |
| Release | : 1989-04-20 |
| Genre | : Mathematics |
| ISBN | : 9782881247057 |
English translation (from revised and enlarged versions of the Russian editions of 1977 and 1984) of a reference work which makes available to engineers, physicists and applied mathematicians theoretical and tabular material pertaining to certain extensions of standard integral transform techniques. Diverse transforms are touched upon, but the emphasis (particularly in the tables) is on generalized Fourier and Laplace transforms. Some multi-dimensional results are presented. Expensive, but nicely produced, and redundant with nothing standard to the reference shelves of mathematical libraries. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
| Author | : R.G. Buschman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 248 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 1461312833 |
It is not the object of the author to present comprehensive cov erage of any particular integral transformation or of any particular development of generalized functions, for there are books available in which this is done. Rather, this consists more of an introductory survey in which various ideas are explored. The Laplace transforma tion is taken as the model type of an integral transformation and a number of its properties are developed; later, the Fourier transfor mation is introduced. The operational calculus of Mikusinski is pre sented as a method of introducing generalized functions associated with the Laplace transformation. The construction is analogous to the construction of the rational numbers from the integers. Further on, generalized functions associated with the problem of extension of the Fourier transformation are introduced. This construction is anal ogous to the construction of the reals from the rationals by means of Cauchy sequences. A chapter with sections on a variety of trans formations is adjoined. Necessary levels of sophistication start low in the first chapter, but they grow considerably in some sections of later chapters. Background needs are stated at the beginnings of each chapter. Many theorems are given without proofs, which seems appro priate for the goals in mind. A selection of references is included. Without showing many of the details of rigor it is hoped that a strong indication is given that a firm mathematical foundation does actu ally exist for such entities as the "Dirac delta-function".
| Author | : A P Prudnikov |
| Publisher | : CRC Press |
| Total Pages | : 424 |
| Release | : 2019-08-30 |
| Genre | : |
| ISBN | : 9780367390495 |
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 advances in the field. Combining the best features of a textbook and a monograph, this volume presents an introduction to operational calculus, integral transforms, and generalized functions, the backbones of pure and applied mathematics. The text examines both the analytical and algebraic aspects of operational calculus and includes a comprehensive survey of classical results while stressing new developments in the field. Among the historical methods considered are Oliver Heaviside's algebraic operational calculus and Paul Dirac's delta function. Other discussions deal with the conditions for the existence of integral transforms, Jan Mikusiński's theory of convolution quotients, operator functions, and the sequential approach to the theory of generalized functions. Benefits... - Discusses theory and applications of integral transforms - Gives inversion, complex-inversion, and Dirac's delta distribution formulas, among others - Offers a short survey of actual results of finite integral transforms, in particular convolution theorems Because Operational Calculus and Related Topics provides examples and illustrates the applications to various disciplines, it is an ideal reference for mathematicians, physicists, scientists, engineers, and students.
| Author | : H. M. Srivastava |
| Publisher | : MDPI |
| Total Pages | : 510 |
| Release | : 2019-11-20 |
| Genre | : Technology & Engineering |
| ISBN | : 303921618X |
Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications
| Author | : Hari Mohan Srivastava |
| Publisher | : MDPI |
| Total Pages | : 220 |
| Release | : 2021-01-20 |
| Genre | : Science |
| ISBN | : 3039368826 |
This volume consists of a collection of 14 accepted submissions (including several invited feature articles) to the Special Issue of MDPI's journal Symmetry on the general subject area of integral transformations, operational calculus and their applications from many different parts around the world. The main objective of the Special Issue was to gather review, expository, and original research articles dealing with the state-of-the-art advances in integral transformations and operational calculus as well as their multidisciplinary applications, together with some relevance to the aspect of symmetry. Various families of fractional-order integrals and derivatives have been found to be remarkably important and fruitful, mainly due to their demonstrated applications in numerous diverse and widespread areas of mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables.
| Author | : V. S. Vladimirov |
| Publisher | : CRC Press |
| Total Pages | : 332 |
| Release | : 2002-08-15 |
| Genre | : Mathematics |
| ISBN | : 9780415273565 |
This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.
| Author | : Thomas K. Boehme |
| Publisher | : Elsevier |
| Total Pages | : 264 |
| Release | : 2014-08-01 |
| Genre | : Mathematics |
| ISBN | : 1483161455 |
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.
