Ram P. Kanwal's Books

Generalized Functions Theory and Technique

Theory and Technique

By: Ram P. Kanwal

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Generalized Functions Theory and Technique

Theory and Technique

By: Ram P. Kanwal

This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.

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474

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468400355

ISBN 13

9781468400359

Linear Integral Equations

Theory and Technique

By: Ram P. Kanwal

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Linear Integral Equations

Theory and Technique

By: Ram P. Kanwal

Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics.

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Page Count

311

Publisher

Academic Press

Published Date

ISBN 10

1483262502

ISBN 13

9781483262505

Singular Integral Equations

By: Ricardo Estrada,Ram P. Kanwal

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Singular Integral Equations

By: Ricardo Estrada,Ram P. Kanwal

Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0

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Page Count

433

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461213827

ISBN 13

9781461213826

Generalized Functions

Theory and Applications

By: Ram P. Kanwal

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Generalized Functions

Theory and Applications

By: Ram P. Kanwal

Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises

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490

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817681744

ISBN 13

9780817681746

A Distributional Approach to Asymptotics

Theory and Applications

By: Ricardo Estrada,Ram P. Kanwal

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A Distributional Approach to Asymptotics

Theory and Applications

By: Ricardo Estrada,Ram P. Kanwal

...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

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467

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817681302

ISBN 13

9780817681302

Asymptotic Analysis

A Distributional Approach

By: Ricardo Estrada,Ram P. Kanwal

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Asymptotic Analysis

A Distributional Approach

By: Ricardo Estrada,Ram P. Kanwal

Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.

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Page Count

266

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468400290

ISBN 13

9781468400298

Book's by Ram P. Kanwal

Generalized Functions Theory and Technique

Generalized Functions Theory and Technique

Linear Integral Equations

Linear Integral Equations

Singular Integral Equations

Singular Integral Equations

Generalized Functions

Generalized Functions

A Distributional Approach to Asymptotics

A Distributional Approach to Asymptotics

Asymptotic Analysis

Asymptotic Analysis

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