Asymptotic Analysis II
Author: F. Verhulst
Publisher: Springer
Published: 2006-11-15
Total Pages: 503
ISBN-13: 3540396128
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Applied Asymptotic Analysis
Author: Peter David Miller
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 488
ISBN-13: 0821840789
DOWNLOAD EBOOKThis 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
Author: J.D. Murray
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 172
ISBN-13: 1461211220
DOWNLOAD EBOOKFrom 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
Author: L. Sirovich
Publisher: Springer Science & Business Media
Published: 1971-03-04
Total Pages: 328
ISBN-13:
DOWNLOAD EBOOK"In this second part of Willie Sugg's history of Cambridgeshire cricket the author focuses on the first documented period of sustained success for a Cambridgeshire club - that of the Cambridge Cricket Club." (back cover) Part two of three.
Asymptotic Analysis and Perturbation Theory
Author: William Paulsen
Publisher: CRC Press
Published: 2013-07-18
Total Pages: 546
ISBN-13: 1466515120
DOWNLOAD EBOOKBeneficial 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 Methods in Analysis
Author: N. G. de Bruijn
Publisher: Courier Corporation
Published: 2014-03-05
Total Pages: 225
ISBN-13: 0486150798
DOWNLOAD EBOOKThis pioneering study/textbook in a crucial area of pure and applied mathematics features worked examples instead of the formulation of general theorems. Extensive coverage of saddle-point method, iteration, and more. 1958 edition.
Asymptotic Analysis of Random Walks
Author: A. A. Borovkov
Publisher: Cambridge University Press
Published: 2020-10-29
Total Pages: 437
ISBN-13: 1108901204
DOWNLOAD EBOOKThis is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Applied and Computational Complex Analysis, Volume 2
Author: Peter Henrici
Publisher: Wiley-Interscience
Published: 1991-03-21
Total Pages: 682
ISBN-13:
DOWNLOAD EBOOKA self-contained presentation of the major areas of complex analysis that are referred to and used in applied mathematics and mathematical physics. Topics discussed include infinite products, ordinary differential equations and asymptotic methods.
Asymptotic Geometric Analysis, Part I
Author: Shiri Artstein-Avidan
Publisher: American Mathematical Soc.
Published: 2015-06-18
Total Pages: 473
ISBN-13: 1470421933
DOWNLOAD EBOOKThe authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.
Asymptotic Analysis
Author: Mikhail V. Fedoryuk
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 370
ISBN-13: 3642580165
DOWNLOAD EBOOKIn 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.
