Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Download Lectures On Non Standard Analysis full books in PDF, epub, and Kindle. Read online Lectures On Non Standard Analysis ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author : Moshe Machover
Publisher : Springer
ISBN 13 : 3540361294
Total Pages : 84 pages
Book Rating : 4.5/5 (43 download)
Download or read book Lectures on Non- Standard Analysis written by Moshe Machover and published by Springer. This book was released on 2007-01-05 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Goldblatt
Publisher : Springer Science & Business Media
ISBN 13 : 1461206154
Total Pages : 292 pages
Book Rating : 4.4/5 (612 download)
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.
Author : Abraham Robinson
Publisher : Princeton University Press
ISBN 13 : 1400884225
Total Pages : 315 pages
Book Rating : 4.4/5 (8 download)
Download or read book Non-standard Analysis written by Abraham Robinson and published by Princeton University Press. This book was released on 2016-08-11 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Author : Mauro Di Nasso
Publisher : Springer
ISBN 13 : 3030179567
Total Pages : 211 pages
Book Rating : 4.0/5 (31 download)
Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.
Author : H. Jerome Keisler
Publisher : Orange Groove Books
ISBN 13 : 9781616100315
Total Pages : 992 pages
Book Rating : 4.1/5 (3 download)
Download or read book Elementary Calculus written by H. Jerome Keisler and published by Orange Groove Books. This book was released on 2009-09-01 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.4/5 (8 download)
Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Author : Dan Sloughter
Publisher : Orange Grove Texts Plus
ISBN 13 : 9781616100896
Total Pages : 0 pages
Book Rating : 4.1/5 (8 download)
Download or read book Yet Another Calculus Text written by Dan Sloughter and published by Orange Grove Texts Plus. This book was released on 2009-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
ISBN 13 : 3642024319
Total Pages : 747 pages
Book Rating : 4.6/5 (42 download)
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author : Tristan Needham
Publisher : Oxford University Press
ISBN 13 : 9780198534464
Total Pages : 620 pages
Book Rating : 4.5/5 (344 download)
Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Author : Kenneth Hoffman
Publisher : Courier Dover Publications
ISBN 13 : 0486833658
Total Pages : 449 pages
Book Rating : 4.4/5 (868 download)
Download or read book Analysis in Euclidean Space written by Kenneth Hoffman and published by Courier Dover Publications. This book was released on 2019-07-17 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.
Author : Robert J. Zimmer
Publisher : University of Chicago Press
ISBN 13 : 0226983382
Total Pages : 169 pages
Book Rating : 4.2/5 (269 download)
Download or read book Essential Results of Functional Analysis written by Robert J. Zimmer and published by University of Chicago Press. This book was released on 1990-01-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
Author : Bernard R. Gelbaum
Publisher : Courier Corporation
ISBN 13 : 0486134911
Total Pages : 226 pages
Book Rating : 4.4/5 (861 download)
Download or read book Counterexamples in Analysis written by Bernard R. Gelbaum and published by Courier Corporation. This book was released on 2012-07-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 147041564X
Total Pages : 354 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 354 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 : Roman Jackiw
Publisher : Springer Science & Business Media
ISBN 13 : 9780387954226
Total Pages : 148 pages
Book Rating : 4.9/5 (542 download)
Download or read book Lectures on Fluid Dynamics written by Roman Jackiw and published by Springer Science & Business Media. This book was released on 2002-05-17 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)
Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Gerald B. Folland
Publisher : John Wiley & Sons
ISBN 13 : 1118626397
Total Pages : 368 pages
Book Rating : 4.1/5 (186 download)
Download or read book Real Analysis written by Gerald B. Folland and published by John Wiley & Sons. This book was released on 2013-06-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
Author : N. L. Carothers
Publisher : Cambridge University Press
ISBN 13 : 9780521497565
Total Pages : 420 pages
Book Rating : 4.4/5 (975 download)
Download or read book Real Analysis written by N. L. Carothers and published by Cambridge University Press. This book was released on 2000-08-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
