Operational Calculus In Two Variables And Its Applications
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Operational Calculus in Two Variables and Its Applications by V.A. Ditkin,A.P. Prudnikov Pdf
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 in Two Variables and Its Applications by V.A. Ditkin,A.P. Prudnikov Pdf
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.
Introduction To The Operational Calculus by Lothar Berg Pdf
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, 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.
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.
Integral Transforms and Their Applications by B. Davies Pdf
This book is intended to serve as introductory and reference material for the application of integral transforms to a range of common mathematical problems. It has its im mediate origin in lecture notes prepared for senior level courses at the Australian National University, although I owe a great deal to my colleague Barry Ninham, a matter to which I refer below. In preparing the notes for publication as a book, I have added a considerable amount of material ad- tional to the lecture notes, with the intention of making the book more useful, particularly to the graduate student - volved in the solution of mathematical problems in the physi cal, chemical, engineering and related sciences. Any book is necessarily a statement of the author's viewpoint, and involves a number of compromises. My prime consideration has been to produce a work whose scope is selective rather than encyclopedic; consequently there are many facets of the subject which have been omitted--in not a few cases after a preliminary draft was written--because I v believe that their inclusion would make the book too long.
Operational Calculus and Generalized Functions by Arthur Erdelyi Pdf
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.
Functions of a Complex Variable and Some of Their Applications by B. A. Fuchs,B. V. Shabat Pdf
Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.
The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory by Thanh Hai Nguyen,Semen B. Yakubovich Pdf
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.
The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory by Nguyen Thanh Hai,S B Yakubovich Pdf
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables. A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals. Contents:General H-Function of Two Variables and the Solution of its Convergence ProblemMain Properties, Series Presentations and Characteristic of the H-FunctionH-Function with the Third Characteristic and its Particular CasesG-Function of Two VariablesTable of Special Cases of the G-FunctionOne-Dimensional H-Transform in Spaces M-1(L) and M-1c,γ(L) and its Composition StructureClassical Laplace Convolution and its New PropertiesGeneral Integral Convolution for H-Function TransformExistence and Factorization Property of the ConvolutionNew Examples of Convolution for Classical Integral TransformsGeneralized Integral ConvolutionGeneral Leibniz Rules and Their Integral Analogs Readership: Researchers and students in mathematics, mechanics and physics. keywords:Mellin Transform of the One and Two Variables;Mellin-Barnes Integrals;Convolutions;Meijer's G-Function of Two Variables;Fox's H-Function of Two Variables;Fourier Transform;Laplace Transform;Gamma Function;Double Kampe de Feriet Hypergeometric Series;Leibniz Rules and Integral Analogs“The book gives a detailed and rigorous account of the theory of double Mellin-Barnes type integrals and contains new fundamental results and their applications to convolution theory. It is a valuable addition to the existing literature in the field of special functions and integral transforms.”K M Saksena “In the areas of special functions and integral transforms, teachers, researchers and graduate students are advised to refer to this work.” Siam Review
Integral Transformations, Operational Calculus and Their Applications by Hari Mohan Srivastava Pdf
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.
