Asymptotic Approximations Of Integrals

Author : R. Wong
Publisher : Academic Press
Page : 561 pages
File Size : 55,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483220710

Get Book

Asymptotic Approximations of Integrals by R. Wong Pdf

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 : Anonim
Publisher : Unknown
Page : 543 pages
File Size : 46,6 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:933997758

Get Book

Asymptotic Approximations of Integrals by Anonim Pdf

Author : Karl W. Breitung
Publisher : Springer
Page : 157 pages
File Size : 48,5 Mb
Release : 2006-11-14
Category : Technology & Engineering
ISBN : 9783540490333

Get Book

Asymptotic Approximations for Probability Integrals by Karl W. Breitung Pdf

This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.

Author : Roderick Wong
Publisher : Boston [Mass.] ; Toronto : Academic Press
Page : 544 pages
File Size : 50,8 Mb
Release : 1989
Category : Mathematics
ISBN : 0127625356

Get Book

Asymptotic Approximations of Integrals by Roderick Wong Pdf

Author : Karl Wilhelm Breitung
Publisher : Springer Verlag
Page : 146 pages
File Size : 44,6 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 0387586172

Get Book

Asymptotic Approximations for Probability Integrals by Karl Wilhelm Breitung Pdf

This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.

Author : Norman Bleistein,Richard A. Handelsman
Publisher : Ardent Media
Page : 456 pages
File Size : 47,7 Mb
Release : 1975
Category : Mathematics
ISBN : 0030835968

Get Book

Asymptotic Expansions of Integrals by Norman Bleistein,Richard A. Handelsman Pdf

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.

Author : Nico M Temme
Publisher : World Scientific
Page : 628 pages
File Size : 50,8 Mb
Release : 2014-10-31
Category : Mathematics
ISBN : 9789814612173

Get Book

Asymptotic Methods for Integrals by Nico M Temme Pdf

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. Contents:Basic Methods for IntegralsBasic Methods: Examples for Special FunctionsOther Methods for IntegralsUniform Methods for IntegralsUniform Methods for Laplace-Type IntegralsUniform Examples for Special FunctionsA Class of Cumulative Distribution Functions Readership: Researchers in applied mathematics, engineering, physics, mathematical statistics, probability theory and biology. The introductory parts and examples will be useful for post-graduate students in mathematics. Key Features:The book gives a complete overview of the classical asymptotic methods for integralsThe many examples give insight in the behavior of the well-known special functionsThe detailed explanations on how to obtain the coefficients in the expansions make the results useful for numerical applications, in particular, for computing special functionsThe many results on asymptotic representations of special functions supplement and extend those in the NIST Handbook of Mathematical FunctionsKeywords:Asymptotic Analysis;Approximation of Integrals;Asymptotic Approximations;Asymptotic Expansions;Steepest Descent Methods;Saddle Point Methods;Stationary Phase Method;Special Functions;Numerical Approximation of Special Functions;Cumulative Distribution FunctionsReviews: “The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt MATH

Author : F. W. J. Olver
Publisher : Academic Press
Page : 312 pages
File Size : 44,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483267081

Get Book

Introduction to Asymptotics and Special Functions by F. W. J. Olver Pdf

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 : R. B. Paris,D. Kaminski
Publisher : Cambridge University Press
Page : 452 pages
File Size : 43,7 Mb
Release : 2001-09-24
Category : Mathematics
ISBN : 1139430122

Get Book

Asymptotics and Mellin-Barnes Integrals by R. B. Paris,D. Kaminski Pdf

Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.

Author : Peter David Miller
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 40,8 Mb
Release : 2006
Category : Approximation theory
ISBN : 9780821840788

Get Book

Applied Asymptotic Analysis by Peter David Miller Pdf

This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entirenonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary. The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and appliedmathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects. The book is ideally suited to the needs of a graduate student who, on the one hand, wants to learn basic applied mathematics, and on the other, wants to understand what is needed to make the various arguments rigorous. Down here in the Village, this is knownas the Courant point of view!! --Percy Deift, Courant Institute, New York Peter D. Miller is an associate professor of mathematics at the University of Michigan at Ann Arbor. He earned a Ph.D. in Applied Mathematics from the University of Arizona and has held positions at the Australian NationalUniversity (Canberra) and Monash University (Melbourne). His current research interests lie in singular limits for integrable systems.

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 44,8 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

Get Book

Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Author : Ovidiu Costin
Publisher : CRC Press
Page : 266 pages
File Size : 53,7 Mb
Release : 2008-12-04
Category : Mathematics
ISBN : 9781420070323

Get Book

Asymptotics and Borel Summability by Ovidiu Costin Pdf

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 : Michael Evans,Timothy Swartz
Publisher : OUP Oxford
Page : 302 pages
File Size : 44,5 Mb
Release : 2000-03-23
Category : Mathematics
ISBN : 9780191589874

Get Book

Approximating Integrals via Monte Carlo and Deterministic Methods by Michael Evans,Timothy Swartz Pdf

This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 41,8 Mb
Release : 1965-12-31
Category : Approximation theory
ISBN : 0821896229

Get Book

Twelve Papers on Approximations and Integrals by Anonim Pdf

Author : Changpin Li,Min Cai
Publisher : SIAM
Page : 326 pages
File Size : 52,5 Mb
Release : 2019-10-31
Category : Mathematics
ISBN : 9781611975888

Get Book

Theory and Numerical Approximations of Fractional Integrals and Derivatives by Changpin Li,Min Cai Pdf

Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus, provides a detailed treatment of existing numerical approximations, and presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.