Download or read book Integral Transforms of Generalized Functions and Their Applications written by Ram Shankar Pathak and published by Routledge. This book was released on 2017-07-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Integral Transforms of Generalized Functions and Their Application written by R.S. Pathak and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Transforms of Generalized Functions written by Brychkov and published by CRC Press. This book was released on 1989-04-20 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Integral Transforms and Their Applications written by Lokenath Debnath and published by CRC Press. This book was released on 2016-04-19 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.
Download or read book Integral Transforms and their Applications written by B. Davies and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In preparing this second edition I have restricted myself to making small corrections and changes to the first edition. Two chapters have had extensive changes made. First, the material of Sections 14.1 and 14.2 has been rewritten to make explicit reference to the book of Bleistein and Handelsman, which appeared after the original Chapter 14 had been written. Second, Chapter 21, on numerical methods, has been rewritten to take account of comparative work which was done by the author and Brian Martin, and published as a review paper. The material for all of these chapters was in fact, prepared for a transla tion of the book. Considerable thought has been given to a much more com prehensive revision and expansion of the book. In particular, there have been spectacular advances in the solution of some non-linear problems using isospectra1 methods, which may be re garded as a generalization of the Fourier transform. However, the subject is a large one, and even a modest introduction would have added substantially to the book. Moreover, the recent book by Dodd et al. is at a similar level to the present volume. Similarly, I have refrained from expanding the chapter on num erical methods into a complete new part of the book, since a specialized monograph on numerical methods is in preparation in collaboration with a colleague.
Download or read book Transform Analysis of Generalized Functions written by O.P. Misra and published by Elsevier. This book was released on 1986-01-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will serve as introductory and reference material for those interested in analysis, applications, physics and engineering.
Download or read book Integral Transforms and Their Applications Third Edition written by Lokenath Debnath and published by CRC Press. This book was released on 2014-11-07 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.
Download or read book Introduction to Hyperfunctions and Their Integral Transforms written by Urs Graf and published by Springer Science & Business Media. This book was released on 2010-03-12 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an introduction to the subject of generalized functions and their integral transforms by an approach based on the theory of functions of one complex variable. It includes many concrete examples.
Download or read book Applications of Fourier Transforms to Generalized Functions written by M. Rahman and published by WIT Press. This book was released on 2011 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized function is one of the important branches of mathematics which has enormous applications in practical fields. In particular its applications to the theory of distribution and signal processing are very much essential. In this computer age, information science plays a very important role and the Fourier transform is extremely significant in deciphering obscured information to be made understandable. The book contains six chapters and three appendices. Chapter 1 deals with the preliminary remarks of Fourier series from general point of view. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. Chapter 4 deals with the asymptotic estimation of Fourier transforms. Chapter 5 is devoted to the study of Fourier series as a series of generalized functions. Chapter 6 deals with the fast Fourier transforms.Appendix A contains the extended list of Fourier transform pairs.Appendix B illustrates the properties of impulse function.Appendix C contains an extended list of biographical references
Download or read book Handbook of Function and Generalized Function Transformations written by Ahmed I. Zayed and published by CRC Press. This book was released on 1996-05-15 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:
Download or read book Generalized Functions and Their Applications written by R.S. Pathak and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.
Download or read book Integral Transformations Operational Calculus and Generalized Functions written by R.G. Buschman and published by Springer. This book was released on 2013-11-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Download or read book Mortality written by Christopher Hitchens and published by Atlantic Books Ltd. This book was released on 2012-08-25 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world's greatest contrarian confronts his own death in this brave and unforgettable book. During the American book tour for his memoir, Hitch-22, Christopher Hitchens collapsed in his hotel room with excruciating pain in his chest. As he would later write in the first of a series of deeply moving Vanity Fair pieces, he was being deported 'from the country of the well across the stark frontier that marks off the land of malady.' Over the next year he experienced the full force of modern cancer treatment. Mortality is at once an unsparingly honest account of the ravages of his disease, an examination of cancer etiquette, and the coda to a lifetime of fierce debate and peerless prose. In this moving personal account of illness, Hitchens confronts his own death - and he is combative and dignified, eloquent and witty to the very last.
Download or read book Integral Transformations Operational Calculus and Generalized Functions written by R.G. Buschman and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Download or read book Methods of the Theory of Generalized Functions written by V. S. Vladimirov and published by CRC Press. This book was released on 2002-08-15 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Integral Transforms written by M. Ya. Antimirov and published by American Mathematical Soc.. This book was released on 2007 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the kernels of integral transforms by solving the generalized Sturm-Liouville problems associated with the partial differential equations at hand. In the first part of the book, the authors construct the kernels and use them to solve elementary problems of mathematical physics. This part requires little mathematical background and provides an introduction to the subject of integral transforms as it proceeds mainly by examples and includes a variety of exercises. In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy-current testing. The choice of topics reflects the authors' research experience and involvement in industrial applications. The first part of the book is accessible to undergraduates, while the second part is aimed at graduate students and researchers. Because of the applications, the book will interest engineers (especially petroleum engineers) and physicists.
Download or read book Asymptotic Behavior of Generalized Functions written by Stevan Pilipovic and published by World Scientific. This book was released on 2012 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.
