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Author : Imme van den Berg
Publisher :
ISBN 13 : 9783662164945
Total Pages : 204 pages
Book Rating : 4.1/5 (649 download)
Download or read book Nonstandard Asymptotic Analysis written by Imme van den Berg and published by . This book was released on 2014-01-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Imme van den Berg
Publisher : Springer
ISBN 13 : 3540478108
Total Pages : 192 pages
Book Rating : 4.5/5 (44 download)
Download or read book Nonstandard Asymptotic Analysis written by Imme van den Berg and published by Springer. This book was released on 2006-11-15 with total page 192 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
Author : Douglas Samuel Jones
Publisher : World Scientific
ISBN 13 : 9789810229153
Total Pages : 184 pages
Book Rating : 4.2/5 (291 download)
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
Author : Douglas S Jones
Publisher : World Scientific
ISBN 13 : 9814497967
Total Pages : 176 pages
Book Rating : 4.8/5 (144 download)
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 176 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.
Author : Alain Robert
Publisher : Courier Corporation
ISBN 13 : 9780486432793
Total Pages : 184 pages
Book Rating : 4.4/5 (327 download)
Download or read book Nonstandard Analysis written by Alain Robert and published by Courier Corporation. This book was released on 2003-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.
Author : Nigel Cutland
Publisher : Cambridge University Press
ISBN 13 : 052135109X
Total Pages : 365 pages
Book Rating : 4.5/5 (213 download)
Download or read book Nonstandard Analysis and Its Applications written by Nigel Cutland and published by Cambridge University Press. This book was released on 1988-09-30 with total page 365 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.
Author : R. Lutz
Publisher : Springer
ISBN 13 : 3540708081
Total Pages : 275 pages
Book Rating : 4.5/5 (47 download)
Download or read book Nonstandard Analysis. written by R. Lutz and published by Springer. This book was released on 2006-11-14 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Imme van den Berg
Publisher : Springer Science & Business Media
ISBN 13 : 3211499059
Total Pages : 415 pages
Book Rating : 4.2/5 (114 download)
Download or read book The Strength of Nonstandard Analysis written by Imme van den Berg and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects the progress made in the forty years since the appearance of Abraham Robinson’s revolutionary book Nonstandard Analysis in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.
Author : Martin Väth
Publisher : Springer Science & Business Media
ISBN 13 : 3764377739
Total Pages : 255 pages
Book Rating : 4.7/5 (643 download)
Download or read book Nonstandard Analysis written by Martin Väth and published by Springer Science & Business Media. This book was released on 2007 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.
Author : Vladimir Kanovei
Publisher : Springer Science & Business Media
ISBN 13 : 366208998X
Total Pages : 421 pages
Book Rating : 4.6/5 (62 download)
Download or read book Nonstandard Analysis, Axiomatically written by Vladimir Kanovei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
Author : Francine Diener
Publisher : Springer Science & Business Media
ISBN 13 : 9783540602972
Total Pages : 268 pages
Book Rating : 4.6/5 (29 download)
Download or read book Nonstandard Analysis in Practice written by Francine Diener and published by Springer Science & Business Media. This book was released on 1995-12-14 with total page 268 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.
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 147041564X
Total Pages : 338 pages
Book Rating : 4.4/5 (74 download)
Download or read book Hilbert's Fifth Problem and Related Topics written by Terence Tao and published by American Mathematical Soc.. This book was released on 2014-07-18 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups. In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.
Author : Nigel J Cutland
Publisher : CRC Press
ISBN 13 : 1000724646
Total Pages : 278 pages
Book Rating : 4.0/5 (7 download)
Download or read book Developments in Nonstandard Mathematics written by Nigel J Cutland and published by CRC Press. This book was released on 2020-01-30 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.
Author : Eduard Yu. Emel'yanov
Publisher : Springer Science & Business Media
ISBN 13 : 3764381140
Total Pages : 181 pages
Book Rating : 4.7/5 (643 download)
Download or read book Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups written by Eduard Yu. Emel'yanov and published by Springer Science & Business Media. This book was released on 2007-02-17 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of operator semigroups. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Related results, historical notes, exercises, and open problems accompany each chapter.
Author : J.E. Rubio
Publisher : CRC Press
ISBN 13 : 9780824792817
Total Pages : 380 pages
Book Rating : 4.7/5 (928 download)
Download or read book Optimization and Nonstandard Analysis written by J.E. Rubio and published by CRC Press. This book was released on 1994-08-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : R. Wong
Publisher : CRC Press
ISBN 13 : 1000154130
Total Pages : 782 pages
Book Rating : 4.0/5 (1 download)
Download or read book Asymptotic and Computational Analysis written by R. Wong and published by CRC Press. This book was released on 2020-12-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented at the International Symposium on Asymptotic and Computational Analysis, held June 1989, Winnipeg, Man., sponsored by the Dept. of Applied Mathematics, University of Manitoba and the Canadian Applied Mathematics Society.
Author : Sergio Albeverio
Publisher : Springer Science & Business Media
ISBN 13 : 9401584516
Total Pages : 255 pages
Book Rating : 4.4/5 (15 download)
Download or read book Advances in Analysis, Probability and Mathematical Physics written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he called `Nonstandard analysis'. `Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics. This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.
