Asymptotic Methods For Integrals
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Asymptotic Methods For Integrals
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Author : Nico M Temme
language : en
Publisher: World Scientific
Release Date : 2014-10-31
Asymptotic Methods For Integrals written by Nico M Temme and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Mathematics categories.
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Asymptotic Expansions Of Integrals
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Author : Norman Bleistein
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01
Asymptotic Expansions Of Integrals written by Norman Bleistein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.
Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Asymptotic Methods For Integrals
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Author : Nico M. Temme
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015
Asymptotic Methods For Integrals written by Nico M. Temme and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Differential equations categories.
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Asymptotic Approximations Of Integrals
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Author : R. Wong
language : en
Publisher: SIAM
Release Date : 2001-01-01
Asymptotic Approximations Of Integrals written by R. Wong and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. The book contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form. Audience: this book can be used either as a text for graduate students in mathematics, physics, and engineering or as a reference for research workers in these fields.
Asymptotic Analysis
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Author : J.D. Murray
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Analysis written by J.D. Murray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
Asymptotic Analysis Of Differential Equations Revised Edition
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Author : Roscoe B White
language : en
Publisher: World Scientific
Release Date : 2010-08-16
Asymptotic Analysis Of Differential Equations Revised Edition written by Roscoe B White and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Mathematics categories.
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.
Asymptotic Expansion Of A Partition Function Related To The Sinh Model
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Author : Gaëtan Borot
language : en
Publisher: Springer
Release Date : 2016-12-08
Asymptotic Expansion Of A Partition Function Related To The Sinh Model written by Gaëtan Borot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Science categories.
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.
Asymptotic Expansions Of Integrals
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Author : Norman Bleistein
language : en
Publisher: Ardent Media
Release Date : 1975
Asymptotic Expansions Of Integrals written by Norman Bleistein and has been published by Ardent Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Coherent, systematic coverage of standard methods: integration by parts, Watson's lemma, LaPlace's method, stationary phase and steepest descents. Also includes Mellin transform method and less elementary aspects of the method of steepest descents. Abundant exercises. 1975 edition.
Computing Highly Oscillatory Integrals
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Author : Alfredo Deano
language : en
Publisher: SIAM
Release Date : 2018-01-01
Computing Highly Oscillatory Integrals written by Alfredo Deano and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-01 with Mathematics categories.
Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety. The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals--Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox--from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis--yet this understanding is the cornerstone of efficient algorithms.