Introduction To Asymptotics A Treatment Using Nonstandard Analysis
DOWNLOAD
Download Introduction To Asymptotics A Treatment Using Nonstandard Analysis PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Introduction To Asymptotics A Treatment Using Nonstandard Analysis book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Introduction To Asymptotics A Treatment Using Nonstandard Analysis
DOWNLOAD
Author : Douglas S Jones
language : en
Publisher: World Scientific
Release Date : 1997-01-16
Introduction To Asymptotics A Treatment Using Nonstandard Analysis written by Douglas S Jones and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-16 with categories.
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hyperasymptotics as well as uniform asymptotics. There are many numerical examples to illustrate the relation between theory and practice. Exercises in the chapters enable the book to be used as a text for an introductory course.
Introduction To Asymptotics
DOWNLOAD
Author : Douglas Samuel Jones
language : en
Publisher: World Scientific
Release Date : 1997
Introduction To Asymptotics written by Douglas Samuel Jones and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
"A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999
Nonstandard Asymptotic Analysis
DOWNLOAD
Author : Imme van den Berg
language : en
Publisher: Springer
Release Date : 2006-11-15
Nonstandard Asymptotic Analysis written by Imme van den Berg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the theory are presented via concrete examples, with many numerical and graphic illustrations. N
Lectures On The Hyperreals
DOWNLOAD
Author : Robert Goldblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On The Hyperreals written by Robert Goldblatt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
Optimization And Nonstandard Analysis
DOWNLOAD
Author : J.E. Rubio
language : en
Publisher: CRC Press
Release Date : 1994-08-10
Optimization And Nonstandard Analysis written by J.E. Rubio and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-10 with Mathematics categories.
This text presents an up-to-date overview of optimization and control theory, including existence theory, modelling, approximation and numerical methods. It also provides a self-contained treatment of the theory and practice of non-standard analysis and its applications, illustrated with problems and research material based on optimization theory. A complete set of detailed exercises and a thorough bibliography arranged by topic are included.;College or university bookstores may order five or more copies at a special student price, available upon request.
Nonstandard Analysis In Practice
DOWNLOAD
Author : Francine Diener
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonstandard Analysis In Practice written by Francine Diener and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals.
Asymptotics And Mellin Barnes Integrals
DOWNLOAD
Author : R. B. Paris
language : en
Publisher: Cambridge University Press
Release Date : 2001-09-24
Asymptotics And Mellin Barnes Integrals written by R. B. Paris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-24 with Mathematics categories.
Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.
Solving Transcendental Equations
DOWNLOAD
Author : John P. Boyd
language : en
Publisher: SIAM
Release Date : 2014-10-23
Solving Transcendental Equations written by John P. Boyd and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-23 with Mathematics categories.
Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute?not always needed, but indispensable when it is. The author?s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding, and it includes three chapters on analytical methods?explicit solutions, regular pertubation expansions, and singular perturbation series (including hyperasymptotics)?unlike other books that give only numerical algorithms for solving algebraic and transcendental equations. This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations.
Hadamard Expansions And Hyperasymptotic Evaluation
DOWNLOAD
Author : R. B. Paris
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-24
Hadamard Expansions And Hyperasymptotic Evaluation written by R. B. Paris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-24 with Mathematics categories.
Describes a new asymptotic method of high-precision evaluation of certain integrals, related to the classical method of steepest descents.
Introduction To Nonstandard Analysis
DOWNLOAD
Author : Vladislav Ėlievich Li︠a︡nt︠s︡e
language : en
Publisher:
Release Date : 1997
Introduction To Nonstandard Analysis written by Vladislav Ėlievich Li︠a︡nt︠s︡e and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Generalized spaces categories.
In Nonstandard Analysis (briefly NSA) there was solved the old problem of substantiation of differential and integral calculus with application of infinitesimals. (This problem seemed to be unsolvable from the times of Leibniz and Euler.) NSA has changed the face of the whole of Mathematics: it is a new mathematical outlook. It is necessary to emphasise that NSA does not object, does not contradict to the Ordinary Mathematics (briefly OM). NSA extends, supplements OM. (This means that all objects, which exist in OM, exist in NSA, too, and all statements which are true in OM retain to be true in NSA.) NSA often simplifies OM and makes it more transparent. NSA states new mathematical theorems and problems. In fact, NSA is a work of the only scientist, namely A. Robinson (1961). His approach to NSA was constructive. In this book we have chosen an axiomatic approach, due to E. Nelson (1977), which is less difficult to learn and apply. (Our exposition, contrary to that of Nelson, is not always strictly logical. Our aim is only some popularization of NSA, and not its foundations.) The text includes some own results of authors. Good supplements to this book are (D-R], [Die], [Lut], [Dav], [Alb], [Cut].