Asymptotic Analysis Of Differential Equations (Revised Edition) PDF Download
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Author: Roscoe B White
Publisher: World Scientific
ISBN: 1911298593
Category : Mathematics
Languages : en
Pages : 430
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Book Description
The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
Author: Roscoe B White
Publisher: World Scientific
ISBN: 1911298593
Category : Mathematics
Languages : en
Pages : 430
Get Book Here
Book Description
The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
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: Frank Olver
Publisher: CRC Press
ISBN: 1439864543
Category : Mathematics
Languages : en
Pages : 591
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Book Description
A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
Author: F. W. J. Olver
Publisher: Academic Press
ISBN: 1483267083
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.
Author: James Dickson Murray
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 156
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Book Description
From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's "Asymptotic" "Expansions" or N.G. de Bruijn's "Asymptotic Methods in" "Analysis" (1958), any academic library would do well to have this excellent introduction." ("S. Puckette, University of" "the South") #"Choice Sept. 1984"#1
Author: Hans G. Kaper
Publisher: CRC Press
ISBN: 1482277069
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Author: Nicholas D. Kazarinoff
Publisher:
ISBN:
Category : Asymptotic distribution (Probability theory)
Languages : en
Pages : 14
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Book Description
Author: Augustin Fruchard
Publisher: Springer
ISBN: 3642340350
Category : Mathematics
Languages : en
Pages : 169
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Book Description
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Author: William Elwood Byerly
Publisher:
ISBN:
Category : Calculus, Integral
Languages : en
Pages : 426
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Book Description
Author: M.H. Lantsman
Publisher: Springer Science & Business Media
ISBN: 9780792371939
Category : Mathematics
Languages : en
Pages : 462
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Book Description
This book is devoted to the asymptotic theory of differential equations. Asymptotic theory is an independent and important branch of mathematical analysis that began to develop at the end of the 19th century. Asymptotic methods' use of several important phenomena of nature can be explained. The main problems considered in the text are based on the notion of an asymptotic space, which was introduced by the author in his works. Asymptotic spaces for asymptotic theory play analogous roles as metric spaces for functional analysis. It allows one to consider many (seemingly) miscellaneous asymptotic problems by means of the same methods and in a compact general form. The book contains the theoretical material and general methods of its application to many partial problems, as well as several new results of asymptotic behavior of functions, integrals, and solutions of differential and difference equations. Audience: The material will be of interest to mathematicians, researchers, and graduate students in the fields of ordinary differential equations, finite differences and functional equations, operator theory, and functional analysis.
