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Introduction To Asymptotics A Treatment Using Nonstandard Analysis

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Introduction To Asymptotics A Treatment Using Nonstandard Analysis

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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

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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

Lectures On The Hyperreals

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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.

There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the course have typically received previous introductions to standard real analysis and abstract algebra, but few have studied formal logic. Most of the notes have been used several times in class and revised in the light of that experience. The earlier chapters could be used as the basis of a course at the upper undergraduate level, but the work as a whole, including the later applications, may be more suited to a beginning graduate course. This prefacedescribes my motivationsand objectives in writingthe book. For the most part, these remarks are addressed to the potential instructor. Mathematical understanding develops by a mysterious interplay between intuitive insight and symbolic manipulation. Nonstandard analysis requires an enhanced sensitivity to the particular symbolic form that is used to ex press our intuitions, and so the subject poses some unique and challenging pedagogical issues. The most fundamental ofthese is how to turn the trans fer principle into a working tool of mathematical practice. I have found it vi Preface unproductive to try to give a proof of this principle by introducing the formal Tarskian semantics for first-order languages and working through the proofofLos's theorem.

Asymptotics And Mellin Barnes Integrals

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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.

Hadamard Expansions And Hyperasymptotic Evaluation

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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.

Solving Transcendental Equations

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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.

A Tour Through Mathematical Logic

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Author : Robert S. Wolf
language : en
Publisher: Cambridge University Press
Release Date : 2005-03-10

A Tour Through Mathematical Logic written by Robert S. Wolf 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 2005-03-10 with Mathematics categories.

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.