Laplace Transforms And An Introduction To Distributions
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Laplace Transforms And An Introduction To Distributions
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Author : Paul B. Guest
language : en
Publisher:
Release Date : 1991
Laplace Transforms And An Introduction To Distributions written by Paul B. Guest and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Laplace transformation categories.
Distribution Theory And Transform Analysis
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Author : A.H. Zemanian
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Distribution Theory And Transform Analysis written by A.H. Zemanian and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Distribution Theory
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Author : Gerrit Dijk
language : en
Publisher: Walter de Gruyter
Release Date : 2013-03-22
Distribution Theory written by Gerrit Dijk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-22 with Mathematics categories.
The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added. It is suitable for a one-semester course at the advanced undergraduate or beginning graduate level or for self-study.
Introduction To The Theory Of Distributions
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Author : F. G. Friedlander
language : en
Publisher: Cambridge University Press
Release Date : 1998
Introduction To The Theory Of Distributions written by F. G. Friedlander and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
The second edition of a classic graduate text on the theory of distributions.
Distribution Theory And Applications
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Author : Abdellah El Kinani
language : en
Publisher: World Scientific
Release Date : 2010
Distribution Theory And Applications written by Abdellah El Kinani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The general frame for the resolution of PDEs is the theory of kernels ù the first elements of which are sufficient to show the practicality of distribution theory in applications. --
Distributions And The Boundary Values Of Analytic Functions
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Author : E. J. Beltrami
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Distributions And The Boundary Values Of Analytic Functions written by E. J. Beltrami and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.
Theory Of Distributions
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Author : Svetlin G. Georgiev
language : en
Publisher: Springer
Release Date : 2015-07-13
Theory Of Distributions written by Svetlin G. Georgiev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-13 with Mathematics categories.
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
Distributions And Their Applications In Physics
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Author : F. Constantinescu
language : en
Publisher: Elsevier
Release Date : 2017-07-26
Distributions And Their Applications In Physics written by F. Constantinescu and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Science categories.
Distributions and Their Applications in Physics is the introduction of the Theory of Distributions and their applications in physics. The book contains a discussion of those topics under the Theory of Distributions that are already considered classic, which include local distributions; distributions with compact support; tempered distributions; the distribution theory in relativistic physics; and many others. The book also covers the Normed and Countably-normed Spaces; Test Function Spaces; Distribution Spaces; and the properties and operations involved in distributions. The text is recommended for physicists that wish to be acquainted with distributions and their relevance and applications as part of mathematical and theoretical physics, and for mathematicians who wish to be acquainted with the application of distributions theory for physics.
An Extension Of The Laplace Transform To Schwartz Distributions
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Author : Douglas B. Price
language : en
Publisher:
Release Date : 1974
An Extension Of The Laplace Transform To Schwartz Distributions written by Douglas B. Price and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Laplace transformation categories.
A new characterization of the Laplace transform is developed which extends the transform to the Schwartz distributions. The class of distributions includes, in addition to all ordinary functions, the impulse functions and other singular functions which occur as solutions to ordinary and partial differential equations. The standard theorems on analyticity, uniqueness, and invertibility of the transform are proved by using the new characterization as the definition of the Laplace transform. The new definition uses sequences of linear transformations on the space of distributions in a manner suggested by a paper of E. Gesztelyi which extended the Laplace transform to another class of generalized functions, the Mikusinski operators. It is shown that the new sequential definition of the transform is equivalent to Schwartz' extension of the ordinary Laplace transform to distributions but, in contrast to Schwartz' definition, does not use the distributional Fourier transform. Several theorems concerning the particular linear transformations used to define the Laplace transforms are proved. All the results proved in one dimension are extended to the n-dimensional case, but proofs are presented only for those situations that require methods different from their one-dimensional analogs.
An Introduction To Distributions
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Author : Aamer Haque
language : en
Publisher: Independently Published
Release Date : 2018-10-12
An Introduction To Distributions written by Aamer Haque and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-12 with Mathematics categories.
Distributions (or generalized functions) allow the possibility of taking derivatives of discontinuousfunctions. There are also distributions which are not generated by ordinary functions. The Dirac deltafunction is an example of a distribution which is not an ordinary function. Unfortunately, most physicsand engineering texts treat it as an ordinary function and skip the formal mathematical definition. Onthe other hand, math books often do not include applications.This book provides a mathematical introduction to the theory of distributions. Most of the importanttheorems are proved. Topics include: Schwartz distributions, tempered distributions, measures, Fouriertransforms, and Laplace transforms. The theory is applied to simple examples in differential equations, probability theory, kinetics, and electrostatics.This graduate level text book is intended for students and researchers in math, science, and engineering.The reader is assumed to have a background in advanced calculus or real analysis