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Introduction To Asymptotics A Treatment Using Nonstandard Analysis
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Book Synopsis Introduction To Asymptotics - A Treatment Using Nonstandard Analysis by : Douglas S Jones
Download or read book Introduction To Asymptotics - A Treatment Using Nonstandard Analysis written by Douglas S Jones and published by World Scientific. This book was released on 1997-01-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Asymptotics by : Douglas Samuel Jones
Download or read book Introduction to Asymptotics written by Douglas Samuel Jones and published by World Scientific. This book was released on 1997 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Book Synopsis Lectures on the Hyperreals by : Robert Goldblatt
Download or read book Lectures on the Hyperreals written by Robert Goldblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotics and Mellin-Barnes Integrals by : R. B. Paris
Download or read book Asymptotics and Mellin-Barnes Integrals written by R. B. Paris and published by Cambridge University Press. This book was released on 2001-09-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hadamard Expansions and Hyperasymptotic Evaluation by : R. B. Paris
Download or read book Hadamard Expansions and Hyperasymptotic Evaluation written by R. B. Paris and published by Cambridge University Press. This book was released on 2011-03-24 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes a new asymptotic method of high-precision evaluation of certain integrals, related to the classical method of steepest descents.
Book Synopsis Nonstandard Asymptotic Analysis by : Imme van den Berg
Download or read book Nonstandard Asymptotic Analysis written by Imme van den Berg and published by Lecture Notes in Mathematics. This book was released on 1987-04-08 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Solving Transcendental Equations by : John P. Boyd
Download or read book Solving Transcendental Equations written by John P. Boyd and published by SIAM. This book was released on 2014-09-23 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 indispensible 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.
Book Synopsis A Tour Through Mathematical Logic by : Robert S. Wolf
Download or read book A Tour Through Mathematical Logic written by Robert S. Wolf and published by Cambridge University Press. This book was released on 2005-03-10 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Progress in Nonlinear Science by : Lev M. Lerman
Download or read book Progress in Nonlinear Science written by Lev M. Lerman and published by . This book was released on 2002 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings written by and published by . This book was released on 2001 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two Studies on Waves in Geophysical Fluids by : Andrei A. Natarov
Download or read book Two Studies on Waves in Geophysical Fluids written by Andrei A. Natarov and published by . This book was released on 2001 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Journal of Symbolic Logic by : Alonzo Church
Download or read book The Journal of Symbolic Logic written by Alonzo Church and published by . This book was released on 1981 with total page 958 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes lists of members.
Book Synopsis Introduction to Nonstandard Analysis by : W. A. J. Luxemburg
Download or read book Introduction to Nonstandard Analysis written by W. A. J. Luxemburg and published by . This book was released on 1974 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonstandard Analysis in Practice by : Francine Diener
Download or read book Nonstandard Analysis in Practice written by Francine Diener and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonstandard Analysis and its Applications by : Nigel Cutland
Download or read book Nonstandard Analysis and its Applications written by Nigel Cutland and published by Cambridge University Press. This book was released on 1988-10-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein
Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
