integral transforms and their applications texts in applied mathematics

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Integral Transforms And Their Applications

Author : B. Davies
ISBN : 9781475755121
Genre : Mathematics
File Size : 45. 19 MB
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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.

Integral Transforms In Applied Mathematics

Author : John W. Miles
ISBN : 0521090687
Genre : Mathematics
File Size : 72. 80 MB
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An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided.

Integral Transforms And Their Applications Third Edition

Author : Lokenath Debnath
ISBN : 9781482223576
Genre : Mathematics
File Size : 86. 73 MB
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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.

Integral Transforms And Their Applications

Author : Lokenath Debnath
ISBN : 0849394589
Genre : Mathematics
File Size : 32. 61 MB
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Integral Transforms and Their Applications, provides a systematic , comprehensive review of the properties of integral transforms and their applications to the solution of boundary and initial value problems. Over 750 worked examples, exercises, and applications illustrate how transform methods can be used to solve problems in applied mathematics, mathematical physics, and engineering. The specific applications discussed include problems in differential, integral, and difference equations; electric circuits and networks; vibrations and wave propagation; heat conduction; fractional derivatives and fractional integrals; dynamical systems; signal processing; quantum mechanics; atmosphere and ocean dynamics; physical chemistry; mathematical biology; and probability and statistics. Integral Transforms and Their Applications includes broad coverage the standard material on integral transforms and their applications, along with modern applications and examples of transform methods. It is both an ideal textbook for students and a sound reference for professionals interested in advanced study and research in the field.

Integral Transforms And Their Applications Third Edition

Author : Lokenath Debnath
ISBN : 9781482223576
Genre : Mathematics
File Size : 32. 76 MB
Format : PDF, ePub, Mobi
Download : 441
Read : 722

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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.

Integral Transforms For Engineers

Author : Larry C. Andrews
ISBN : 0819432326
Genre : Mathematics
File Size : 82. 5 MB
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Integral transform methods provide effective ways to solve a variety of problems arising in the engineering, optical, and physical sciences. Suitable as a self-study for practicing engineers and applied mathematicians and as a textbook in graduate-level courses in optics, engineering sciences, physics, and mathematics.

Integral Transforms Of Generalized Functions And Their Applications

Author : Ram Shankar Pathak
ISBN : 9781351562690
Genre : History
File Size : 41. 99 MB
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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.

Local Fractional Integral Transforms And Their Applications

Author : Xiao Jun Yang
ISBN : 9780128040324
Genre : Mathematics
File Size : 70. 65 MB
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Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods

Applied Integral Transforms

Author : M. Ya. Antimirov
ISBN : 0821843141
Genre : Mathematics
File Size : 58. 93 MB
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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. 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 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.

Wavelet Transforms And Their Applications

Author : Lokenath Debnath
ISBN : 9780817684181
Genre : Technology & Engineering
File Size : 44. 43 MB
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This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.

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