Applied Asymptotics PDF Download
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| Author | : Peter David Miller |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 488 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821840789 |
Download Applied Asymptotic Analysis Book in PDF, ePub and Kindle
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 | : A. R. Brazzale |
| Publisher | : Cambridge University Press |
| Total Pages | : 256 |
| Release | : 2007-05-31 |
| Genre | : Business & Economics |
| ISBN | : 9780521847032 |
Download Applied Asymptotics Book in PDF, ePub and Kindle
First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.
| Author | : Ovidiu Costin |
| Publisher | : CRC Press |
| Total Pages | : 266 |
| Release | : 2008-12-04 |
| Genre | : Mathematics |
| ISBN | : 1420070320 |
Download Asymptotics and Borel Summability Book in PDF, ePub and Kindle
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 | : Norman Bleistein |
| Publisher | : Courier Corporation |
| Total Pages | : 453 |
| Release | : 1986-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486650820 |
Download Asymptotic Expansions of Integrals Book in PDF, ePub and Kindle
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.
| Author | : A. W. van der Vaart |
| Publisher | : Cambridge University Press |
| Total Pages | : 470 |
| Release | : 2000-06-19 |
| Genre | : Mathematics |
| ISBN | : 9780521784504 |
Download Asymptotic Statistics Book in PDF, ePub and Kindle
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.
| Author | : David Holcman |
| Publisher | : Springer |
| Total Pages | : 444 |
| Release | : 2018-05-25 |
| Genre | : Mathematics |
| ISBN | : 3319768956 |
Download Asymptotics of Elliptic and Parabolic PDEs Book in PDF, ePub and Kindle
This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.
| Author | : R. Wong |
| Publisher | : Academic Press |
| Total Pages | : 561 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483220710 |
Download Asymptotic Approximations of Integrals Book in PDF, ePub and Kindle
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 | : A. R. Brazzale |
| Publisher | : Cambridge University Press |
| Total Pages | : 211 |
| Release | : 2007-05-31 |
| Genre | : Mathematics |
| ISBN | : 1139463837 |
Download Applied Asymptotics Book in PDF, ePub and Kindle
In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.
| Author | : Anirban DasGupta |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 726 |
| Release | : 2008-03-07 |
| Genre | : Mathematics |
| ISBN | : 0387759700 |
Download Asymptotic Theory of Statistics and Probability Book in PDF, ePub and Kindle
This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
| Author | : G. I. Barenblatt |
| Publisher | : Cambridge University Press |
| Total Pages | : 412 |
| Release | : 1996-12-12 |
| Genre | : Mathematics |
| ISBN | : 9780521435222 |
Download Scaling, Self-similarity, and Intermediate Asymptotics Book in PDF, ePub and Kindle
Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.
