Asymptotic Analysis


Asymptotic Analysis
Author: J.D. Murray
Publisher: Springer Science & Business Media
ISBN: 1461211220
Size: 11.68 MB
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Asymptotic Analysis

eBook File: Asymptotic-analysis.PDF Book by J.D. Murray, Asymptotic Analysis Books available in PDF, EPUB, Mobi Format. Download Asymptotic Analysis books, 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
Language: en
Pages: 165
Authors: J.D. Murray
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
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 for Periodic Structures
Language: en
Pages: 392
Authors: Alain Bensoussan, Jacques-Louis Lions, George Papanicolaou
Categories: Mathematics
Type: BOOK - Published: 2011-10-26 - Publisher: American Mathematical Soc.
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
Asymptotic Analysis
Language: en
Pages: 363
Authors: Mikhail V. Fedoryuk
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Applied Asymptotic Analysis
Language: en
Pages: 467
Authors: Peter David Miller
Categories: Mathematics
Type: BOOK - Published: 2006 - Publisher: American Mathematical Soc.
"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.
Asymptotic Analysis of Singular Perturbations
Language: en
Pages: 286
Authors: W. Eckhaus
Categories: Mathematics
Type: BOOK - Published: 2011-08-30 - Publisher: Elsevier
Asymptotic Analysis of Singular Perturbations
Asymptotic Analysis
Language: en
Pages: 248
Authors: F. Verhulst
Categories: Mathematics
Type: BOOK - Published: 2006-11-15 - Publisher: Springer
Books about Asymptotic Analysis
Asymptotic Analysis Of Differential Equations (Revised Edition)
Language: en
Pages: 432
Authors: White Roscoe B
Categories: Mathematics
Type: BOOK - Published: 2010-08-16 - Publisher: World Scientific
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.
Exam Prep for: Non-asymptotic Analysis of Approximations ...
Language: en
Pages:
Authors: White Roscoe B
Categories: Mathematics
Type: - Published: - Publisher:
Books about Exam Prep for: Non-asymptotic Analysis of Approximations ...
Asymptotic Analysis
Language: en
Pages: 258
Authors: Ricardo Estrada, Ram P. Kanwal
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide
Asymptotic Analysis of Random Walks
Language: en
Pages: 625
Authors: A. A. Borovkov, K. A. Borovkov
Categories: Mathematics
Type: BOOK - Published: 2008-06-12 - Publisher: Cambridge University Press
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.