Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase (Classic Reprint) - Softcover

Jones, Douglas S.

9781332102518: Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase (Classic Reprint)

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ISBN 10: 1332102514 ISBN 13: 9781332102518

Verlag: Forgotten Books, 2015

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Excerpt from Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase

To obtain such a result Van Kampen[h] applied the method of stationary phase, originally developed for single integrals, in a purely formal manner. It is clear from the formal uses of the method of stationary phase that the asymptotic series representation of (l) is a sum of asymptotic series determined by the behavior of f(x,y) in the neighborhood of certain critical points of the domain D of integra tion.

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Verlag: Forgotten Books
Erscheinungsdatum: 2015
Sprache: Englisch
ISBN 10: 1332102514
ISBN 13: 9781332102518
Einband: Taschenbuch
Anzahl der Seiten: 60
Kontakt zum Hersteller: Nicht verf�gbar
Verantwortliche Person: Nicht verf�gbar

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Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase

Douglas S. Jones, Morris Kline

Verlag: Forgotten Books, 2018

ISBN 10: 1332102514 ISBN 13: 9781332102518

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Paperback. Zustand: New. Print on Demand. This book delves into the fascinating world of asymptotic expansion of multiple integrals, a complex mathematical concept that holds significant implications for fields like diffraction theory in optics and microwave problems. The author takes a unique approach by reducing the evaluation of these integrals to a more manageable problem of evaluating single Fourier integrals. This simplification allows for a more streamlined analysis of the asymptotic behavior of the integral, which is particularly crucial when dealing with situations involving small wavelengths or large values of k, a parameter frequently encountered in physical applications. The book's exploration of asymptotic expansion is not merely a theoretical exercise. It presents a clear link between the behavior of contour lines, represented by the equation f(x,y) = constant, and the critical points within the domain of integration. These contour lines hold direct physical significance, particularly in diffraction optics where they represent the optical distance from a source to a point in the image space. By understanding the interplay between these lines and critical points, the author sheds light on the intricate nature of diffraction phenomena and the contribution of various critical points to the overall behavior of the field. The book's meticulous examination of the mathematical framework and its tangible applications in diverse scientific domains makes it an invaluable resource for anyone interested in understanding the depths of asymptotic analysis and its practical implications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verk�ufers 9781332102518_0

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