• Mathematics

Applied Asymptotic Analysis


Author: Peter David Miller
Publisher: American Mathematical Soc.
ISBN: 0821840789
Category: Mathematics
Page: 467
View: 3845
"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics 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."--BOOK JACKET.

    • Mathematics

Applied Asymptotic Analysis


Author: Peter David Miller
Publisher: American Mathematical Soc.
ISBN: 9780821872451
Category: Mathematics
Page: 467
View: 7210
"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics 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."--BOOK JACKET.

    • Mathematics

Asymptotic Analysis


Author: J.D. Murray
Publisher: Springer Science & Business Media
ISBN: 1461211220
Category: Mathematics
Page: 165
View: 7141
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

    • Mathematics

Asymptotic Analysis and Perturbation Theory


Author: William Paulsen
Publisher: CRC Press
ISBN: 1466515120
Category: Mathematics
Page: 550
View: 2396
Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge of differential equations. It explains the exact solution of only the simplest differential equations, such as first-order linear and separable equations. With varying levels of problems in each section, this self-contained text makes the difficult subject of asymptotics easy to comprehend. Along the way, it explores the properties of some important functions in applied mathematics. Although the book emphasizes problem solving, some proofs are scattered throughout to give readers a justification for the methods used.

    • Mathematics

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations


Author: Hans G. Kaper,Marc Garbey
Publisher: CRC Press
ISBN: 9780585319674
Category: Mathematics
Page: 286
View: 9081
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

    • Mathematics

Asymptotic Analysis of Mixed Effects Models

Theory, Applications, and Open Problems
Author: Jiming Jiang
Publisher: CRC Press
ISBN: 1351645595
Category: Mathematics
Page: 252
View: 8212
Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.

    • Mathematics

Asymptotic Methods for Integrals


Author: Nico M Temme
Publisher: World Scientific
ISBN: 9814612170
Category: Mathematics
Page: 628
View: 600
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

    • Mathematics

Nonlinear Dispersive Waves

Asymptotic Analysis and Solitons
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 1139503480
Category: Mathematics
Page: N.A
View: 6620
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

    • Mathematics

Asymptotic Expansions


Author: E. T. Copson,Edward Thomas Copson
Publisher: Cambridge University Press
ISBN: 9780521604826
Category: Mathematics
Page: 120
View: 7676
Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.

    • Mathematics

Asymptotic Approximations of Integrals

Computer Science and Scientific Computing
Author: R. Wong
Publisher: Academic Press
ISBN: 1483220710
Category: Mathematics
Page: 556
View: 5739
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.

    • Mathematics

Asymptotic Analysis for Periodic Structures


Author: Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou
Publisher: American Mathematical Soc.
ISBN: 0821853244
Category: Mathematics
Page: 392
View: 4799
This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.

    • Mathematics

Techniques of Asymptotic Analysis


Author: Lawrence Sirovich
Publisher: Springer Science & Business Media
ISBN: 1461264022
Category: Mathematics
Page: 306
View: 5596
These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. In the hope that these notes might prove useful for reference purposes several additional sections have been included and also a table of contents and index. Although asymptotic analysis is now enjoying a period of great vitality, these notes do not reflect a research oriented course. The course is aimed toward people in applied mathematics, physics, engineering, etc., who have a need for asymptotic analysis in their work. The choice of subjects has been largely dictated by the likelihood of application. Also abstraction and generality have not been pursued. Technique and computation are given equal prominence with theory. Both rigorous and formal theory is presented --very often in tandem. In practice, the means for a rigorous analysis are not always available. For this reason a goal has been the cultivation of mature formal reasoning. Therefore, during the course of lectures formal presentations gradually eclipse rigorous presentations. When this occurs, rigorous proofs are given as exercises or in the case of lengthy proofs, reference is made to the Reading List at the end.

    • Mathematics

Normal Approximation and Asymptotic Expansions


Author: Rabi N. Bhattacharya,R. Ranga Rao
Publisher: SIAM
ISBN: 089871897X
Category: Mathematics
Page: 316
View: 7711
-Fourier analysis, --

    • Mathematics

Asymptotic Analysis of Differential Equations


Author: R. B. White
Publisher: World Scientific
ISBN: 1848166087
Category: Mathematics
Page: 405
View: 6794
"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.

    • Mathematics

Plates, Laminates, and Shells

Asymptotic Analysis and Homogenization
Author: T. Lewi?ski,J¢zef Joachim Telega
Publisher: World Scientific
ISBN: 9789810232061
Category: Mathematics
Page: 739
View: 8123
This book gives a systematic and comprehensive presentation of the results concerning effective behavior of elastic and plastic plates with periodic or quasiperiodic structure. One of the chapters covers the hitherto available results concerning the averaging problems in the linear and nonlinear shell models.A unified approach to the problems studied is based on modern variational and asymptotic methods, including the methods of variational inequalities as well as homogenization techniques. Duality arguments are also exploited. A significant part of the book deals with problems important for engineering practice, such as: statical analysis of highly nonhomogeneous plates and shells for which common discretization techniques fail to be efficient, assessing stiffness reduction of cracked 0n/900m]s laminates, and assessing ultimate loads for perfectly plastic plates and shells composed of repeated segments. When possible, the homogenization formulas are cast in closed form expressions. The formulas presented in this manner are then used in constructing regularized formulations of the fundamental optimization problems for plates and shells, since the regularization concepts are based on introducing the composite regions for which microstructural properties play the role of new design variables.

    • Mathematics

Asymptotic Analysis of Singular Perturbations


Author: W. Eckhaus
Publisher: Elsevier
ISBN: 9780080875309
Category: Mathematics
Page: 286
View: 5322
Asymptotic Analysis of Singular Perturbations

    • Mathematics

From Finite Sample to Asymptotic Methods in Statistics


Author: Pranab K. Sen,Julio M. Singer,Antonio C. Pedroso de Lima
Publisher: Cambridge University Press
ISBN: 0521877229
Category: Mathematics
Page: 386
View: 8833
A broad view of exact statistical inference and the development of asymptotic statistical inference.

    • Mathematics

Asymptotics and Borel Summability


Author: Ovidiu Costin
Publisher: CRC Press
ISBN: 9781420070323
Category: Mathematics
Page: 256
View: 3116
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, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers. To give a sense of how new methods are used in a systematic way, the book analyzes in detail general nonlinear ordinary differential equations (ODEs) near a generic irregular singular point. It enables readers to master basic techniques, supplying a firm foundation for further study at more advanced levels. The book also examines difference equations, partial differential equations (PDEs), and other types of problems. Chronicling the progress made in recent decades, this book shows how Borel summability can recover exact solutions from formal expansions, analyze singular behavior, and vastly improve accuracy in asymptotic approximations.

    • Mathematics

Asymptotic Expansions of Integrals


Author: Norman Bleistein,Richard A. Handelsman
Publisher: Courier Corporation
ISBN: 0486650820
Category: Mathematics
Page: 425
View: 2280
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.

    • Mathematics

Matched Asymptotic Expansions

Ideas and Techniques
Author: P.A. Lagerstrom
Publisher: Springer Science & Business Media
ISBN: 1475719906
Category: Mathematics
Page: 252
View: 6833
Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.