Asymptotic Expansions: Their Derivation and Interpretation PDF Download

Author: Robert B. Dingle
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 556

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Author: Ovidiu Costin
Publisher: CRC Press
ISBN: 1420070320
Category : Mathematics
Languages : en
Pages : 266

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Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr

Author: Rudrapatna V. Ramnath
Publisher: Springer Science & Business Media
ISBN: 3642257496
Category : Technology & Engineering
Languages : en
Pages : 126

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Book Description
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of different scales in a dynamic phenomenon enable us to make judicious use of them in developing computational approaches which are highly efficient. Many such applications have been developed in such areas as astrodynamics, fluid mechanics and so on. This book presents a novel approach to make use of the different time constants inherent in the system to develop rapid computational methods. First, the fundamental notions of asymptotic analysis are presented with classical examples. Next, the novel systematic and rigorous approaches of system decomposition and reduced order models are presented. Next, the technique of multiple scales is discussed. Finally application to rapid computation of several aerospace systems is discussed, demonstrating the high efficiency of such methods.

Author: R. B. White
Publisher: World Scientific
ISBN: 1848166079
Category : Mathematics
Languages : en
Pages : 430

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"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

Author: R. Wong
Publisher: Academic Press
ISBN: 1483220710
Category : Mathematics
Languages : en
Pages : 561

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Book Description
Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

Author: F. W. J. Olver
Publisher: Academic Press
ISBN: 148326744X
Category : Mathematics
Languages : en
Pages : 589

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Book Description
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.

Author: Max Born
Publisher: Cambridge University Press
ISBN: 1108477437
Category : Science
Languages : en
Pages : 993

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Book Description
The 60th anniversary edition of this classic and unrivalled optics reference work includes a special foreword by Sir Peter Knight.

Author: Derek Richards
Publisher: Cambridge University Press
ISBN: 9780521779814
Category : Computers
Languages : en
Pages : 884

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Book Description
A user-friendly student guide to computer-assisted algebra with mathematical software packages such as Maple.

Author: Frank W. J. Olver
Publisher: World Scientific
ISBN: 9789810249953
Category : Asymptotic expansions
Languages : en
Pages : 568

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Author: Mark McCartney
Publisher:
ISBN: 0198822863
Category : Biography & Autobiography
Languages : en
Pages : 264

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Book Description
George Gabriel Stokes was one of the most important mathematical physicists of the 19th century. During his lifetime he made a wide range of contributions, notably in continuum mechanics, optics and mathematical analysis. His name is known to generations of scientists and engineers through the various physical laws and mathematical formulae named after him, such as the Navier-Stokes equations in fluid dynamics. Born in Ireland into a family of academics, clergymen and physicians, he became the longest serving Lucasian Professor of Mathematics at Cambridge. Impressive as his own scientific achievements were, he made an equally important contribution as a sounding board for his contemporaries, providing good judgement and mathematical rigour in his wide correspondence and during his 31 years as Secretary of the Royal Society where he played a major role in the direction of British science. Outside his own area he was a distinguished public servant and MP for Cambridge University. He was keenly interested in the relation between science and religion and wrote at length on their interaction. Stokes was a remarkable scientist who lived in an equally remarkable age of discovery and innovation. This edited collection of essays brings together experts in mathematics, physics and the history of science to cover the many facets of Stokes's life in a scholarly but accessible way to mark the bicentenary of his birth.