Applied Asymptotic Analysis

Applied Asymptotic Analysis Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Applied Asymptotic Analysis book. This book definitely worth reading, it is an incredibly well-written.

Applied Asymptotic Analysis

Peter David Miller
Applied Asymptotic Analysis Book PDF

Author : Peter David Miller
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 48,9 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.

Asymptotic Analysis

J.D. Murray
Asymptotic Analysis Book PDF

Author : J.D. Murray
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211228

Get Book

Asymptotic Analysis by J.D. Murray Pdf

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

Techniques of Asymptotic Analysis

Lawrence Sirovich
Techniques of Asymptotic Analysis Book PDF

Author : Lawrence Sirovich
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 46,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461264026

Get Book

Techniques of Asymptotic Analysis by Lawrence Sirovich Pdf

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.

Asymptotic Analysis and Perturbation Theory

William Paulsen
Asymptotic Analysis and Perturbation Theory Book PDF

Author : William Paulsen
Publisher : CRC Press
Page : 550 pages
File Size : 47,8 Mb
Release : 2013-07-18
Category : Mathematics
ISBN : 9781466515123

Get Book

Asymptotic Analysis and Perturbation Theory by William Paulsen Pdf

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 o

Asymptotic Expansions of Integrals

Norman Bleistein,Richard A. Handelsman
Asymptotic Expansions of Integrals Book PDF

Author : Norman Bleistein,Richard A. Handelsman
Publisher : Courier Corporation
Page : 453 pages
File Size : 40,8 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 9780486650821

Get Book

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

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.

Applied Asymptotic Expansions in Momenta and Masses

Vladimir A. Smirnov
Applied Asymptotic Expansions in Momenta and Masses Book PDF

Author : Vladimir A. Smirnov
Publisher : Springer
Page : 265 pages
File Size : 40,8 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540445746

Get Book

Applied Asymptotic Expansions in Momenta and Masses by Vladimir A. Smirnov Pdf

'The sturgeon they sent was second grade fresh,' said the barman. 'Really, what nonsense/' 'Why nonsense?' '"Second grade fresh" that's what I call nonsense/ There's only one degree of freshness the first, and it's the last) (M. A. Bulgakov, The Master and Margarita) The goal of this book is to describe in detail how Feynman integrals can be expanded in suitable parameters, when various momenta or masses are small or large. In a narrow sense, this problem is connected with practical calcula tions. In a situation where a given Feynman integral depends on parameters of very different scales, a natural idea is to replace it by a sufficiently large number of terms of an expansion of it in ratios of small and large scales. It will be explained how this problem of expansion can be systematically solved, by formulating universal prescriptions that express terms of the expansion by using the original Feynman integral with its integrand expanded into a Taylor series in appropriate momenta and masses. It turns out that knowledge of the structure of the asymptotic expansion at the diagrammatic level is a key point in understanding how to perform expansions at the operator level. There are various examples of these ex pansions: the operator product expansion, the large mass expansion, Heavy Quark Effective Theory, Non Relativistic QCD, etc. Each of them serves as a realization of the factorization of contributions of different scales.

Asymptotic Analysis Of Differential Equations (Revised Edition)

White Roscoe B
Asymptotic Analysis Of Differential Equations Revised Edition Book PDF

Author : White Roscoe B
Publisher : World Scientific
Page : 432 pages
File Size : 53,9 Mb
Release : 2010-08-16
Category : Mathematics
ISBN : 9781911298595

Get Book

Asymptotic Analysis Of Differential Equations (Revised Edition) by White Roscoe B Pdf

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.

Asymptotics and Borel Summability

Ovidiu Costin
Asymptotics and Borel Summability Book PDF

Author : Ovidiu Costin
Publisher : CRC Press
Page : 256 pages
File Size : 52,6 Mb
Release : 2008-12-04
Category : Mathematics
ISBN : 1420070320

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, 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.

Matched Asymptotic Expansions

P.A. Lagerstrom
Matched Asymptotic Expansions Book PDF

Author : P.A. Lagerstrom
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 50,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719901

Get Book

Matched Asymptotic Expansions by P.A. Lagerstrom Pdf

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.

Asymptotic Analysis for Functional Stochastic Differential Equations

Jianhai Bao,George Yin,Chenggui Yuan
Asymptotic Analysis for Functional Stochastic Differential Equations Book PDF

Author : Jianhai Bao,George Yin,Chenggui Yuan
Publisher : Springer
Page : 151 pages
File Size : 52,9 Mb
Release : 2016-11-19
Category : Mathematics
ISBN : 9783319469799

Get Book

Asymptotic Analysis for Functional Stochastic Differential Equations by Jianhai Bao,George Yin,Chenggui Yuan Pdf

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Asymptotic Methods for Relaxation Oscillations and Applications

Johan Grasman
Asymptotic Methods for Relaxation Oscillations and Applications Book PDF

Author : Johan Grasman
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461210566

Get Book

Asymptotic Methods for Relaxation Oscillations and Applications by Johan Grasman Pdf

In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.

Asymptotic Analysis and Boundary Layers

Jean Cousteix,Jacques Mauss
Asymptotic Analysis and Boundary Layers Book PDF

Author : Jean Cousteix,Jacques Mauss
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 51,8 Mb
Release : 2007-03-22
Category : Science
ISBN : 9783540464891

Get Book

Asymptotic Analysis and Boundary Layers by Jean Cousteix,Jacques Mauss Pdf

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

Introduction to Asymptotic Methods

David Y. Gao,Vadim A. Krysko
Introduction to Asymptotic Methods Book PDF

Author : David Y. Gao,Vadim A. Krysko
Publisher : CRC Press
Page : 272 pages
File Size : 40,7 Mb
Release : 2006-05-03
Category : Mathematics
ISBN : 9781420011739

Get Book

Introduction to Asymptotic Methods by David Y. Gao,Vadim A. Krysko Pdf

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m

Borel-Laplace Transform and Asymptotic Theory

Boris Yu. Sternin,Victor E. Shatalov
Borel Laplace Transform and Asymptotic Theory Book PDF

Author : Boris Yu. Sternin,Victor E. Shatalov
Publisher : CRC Press
Page : 284 pages
File Size : 45,7 Mb
Release : 1995-10-20
Category : Mathematics
ISBN : 084939435X

Get Book

Borel-Laplace Transform and Asymptotic Theory by Boris Yu. Sternin,Victor E. Shatalov Pdf

The resurgent function theory introduced by J. Ecalle is one of the most interesting theories in mathematical analysis. In essence, the theory provides a resummation method for divergent power series (e.g., asymptotic series), and allows this method to be applied to mathematical problems. This new book introduces the methods and ideas inherent in resurgent analysis. The discussions are clear and precise, and the authors assume no previous knowledge of the subject. With this new book, mathematicians and other scientists can acquaint themselves with an interesting and powerful branch of asymptotic theory - the resurgent functions theory - and will learn techniques for applying it to solve problems in mathematics and mathematical sciences.

Asymptotic Analysis for Periodic Structures

Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou
Asymptotic Analysis for Periodic Structures Book PDF

Author : Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 44,6 Mb
Release : 2011-10-26
Category : Mathematics
ISBN : 9780821853245

Get Book

Asymptotic Analysis for Periodic Structures by Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou Pdf

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.