Download PDF Asymptotic Expansions of Integrals (Dover Books on Mathematics), by Norman Bleistein, Richard A Handelsman
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Asymptotic Expansions of Integrals (Dover Books on Mathematics), by Norman Bleistein, Richard A Handelsman
Download PDF Asymptotic Expansions of Integrals (Dover Books on Mathematics), by Norman Bleistein, Richard A Handelsman
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Asymptotic analysis, that branch of mathematics devoted to the study of the behavior of functions within chosen limits, was once thought of more as a specialized art than a necessary discipline. Now, a solid foundation in the theory and technique of asymptotic expansion of integrals is at the heart of the education of every student concentrating in applied mathematics. It is also an invaluable asset to scientists in many other fields.This excellent introductory text, written by two experts in the field, offers students of applied mathematics — and researchers and workers in other fields — a coherent and systematic presentation of the principles and methods of asymptotic expansions of integrals. Students will find each of the nine chapters useful and easy to comprehend; each begins with elementary material or informal introductions and concludes with an abundant selection of applicable problems and exercises. All that is needed is a basic understanding of calculus, differential equations, and complex variables.Practiced users of asymptotics will find the work a valuable reference with an extensive index locating all the functions covered in the text and every formula associated with the major techniques. Subjects include integration by parts, Watson's lemma, Laplace's method, stationary phase, and steepest descents. Also treated are the Mellin transform method and less elementary aspects of steepest descent. Each chapter is carefully illustrated with helpful diagrams and tables.Used for years as a text in classrooms throughout the country, the book has been revised and corrected for this inexpensive paperback edition. Any student or teacher looking for a suitable text for a year's or semester's course in asymptotics will value this affordable volume as the only comprehensive introduction available; scientists and researchers will undoubtedly refer to it again and again.
- Sales Rank: #1163283 in Books
- Published on: 2010-11-18
- Released on: 2010-10-21
- Original language: English
- Number of items: 1
- Dimensions: 8.47" h x .84" w x 5.41" l, 1.03 pounds
- Binding: Paperback
- 464 pages
From the Back Cover
Asymptotic analysis, that branch of mathematics devoted to the study of the behavior of functions within chosen limits, was once thought of more as a specialized art than a necessary discipline. Now, a solid foundation in the theory and technique of asymptotic expansion of integrals is at the heart of the education of every student concentrating in applied mathematics. It is also an invaluable asset to scientists in many other fields.This excellent introductory text, written by two experts in the field, offers students of applied mathematics — and researchers and workers in other fields — a coherent and systematic presentation of the principles and methods of asymptotic expansions of integrals. Students will find each of the nine chapters useful and easy to comprehend; each begins with elementary material or informal introductions and concludes with an abundant selection of applicable problems and exercises. All that is needed is a basic understanding of calculus, differential equations, and complex variables.Practiced users of asymptotics will find the work a valuable reference with an extensive index locating all the functions covered in the text and every formula associated with the major techniques. Subjects include integration by parts, Watson's lemma, Laplace's method, stationary phase, and steepest descents. Also treated are the Mellin transform method and less elementary aspects of steepest descent. Each chapter is carefully illustrated with helpful diagrams and tables.Used for years as a text in classrooms throughout the country, the book has been revised and corrected for this inexpensive paperback edition. Any student or teacher looking for a suitable text for a year's or semester's course in asymptotics will value this affordable volume as the only comprehensive introduction available; scientists and researchers will undoubtedly refer to it again and again.
Unabridged, corrected Dover (1986) republication of the edition published by Holt, Rinehart and Winston, New York, 1975.
Most helpful customer reviews
17 of 18 people found the following review helpful.
Excellent !!!
By A Customer
The book contains valuable information about a specialized area of applied mathematics. The material presented in this book is applicable to problems involving quantum and electromagtnetic scattering at high frequencies. In the area of radar technology, the radar cross-section of a target is calculated using asymptotic evaluation of Fourier integrals that appear in the final form of the electric and magnetic field vectors following a solution to the appropriate boundary value problem, starting with Maxwell's equations.
To study the book, the reader must have had course on complex variables upto and including residue theory, infinite series, analytic continuation, conformal mapping and multivalued functions, plus a introductory knowledge of ordinary differential equations.
Without discussing the contents of each chapter, I can only comment that they are most lucid and intellectually satisfying; in particular chaps. 7 and 9 are most useful to practical problems
The contents of chapters 7 and 9 are widely applicable in various electrical engineering problems - short-pulse radars, high-frequnecy scattering, antenna theory and the like. The main advantage of using these asymptotic methods is that they reduce spectral integrals stemming from potential theory (Green's functions) are to " almost " closed form solutions that are not exact but computationally extremely helpful. In many cases, for example EM scattering by a circular cylinder, numerical results can only be obtained if asymptotic methods are applied at high frequencies. The use of asymptotic methods in engineering computation is primarily to reduce the c.p.u. time by several orders of magnitude as compared to exact calculations. This allows faster and more efficient solution to problems. The book is well organized and there are enough homework problems for the interested reader. A must pre-requisite for understanding the topic(s) is a reasonably good grasp of the theory functions of a complex variable, as mentioned at the begining of this review.
0 of 0 people found the following review helpful.
great!
By Reviewer321
well, a great complete book by master of asymptotic. not simple, but you gain a lot.
0 of 2 people found the following review helpful.
I like this book
By Paulo finardi
I like this book, For me is the 2nd vest of Bleistein, the number one is Mathmatics of Multidimension Seismic Imaging Migration, and Inversion.
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