The Way Of Analysis
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The Way Of Analysis
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Author : Robert S. Strichartz
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2000
The Way Of Analysis written by Robert S. Strichartz and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.
The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.
Understanding Analysis
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Author : Stephen Abbott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Understanding Analysis written by Stephen Abbott 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.
Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage, the hard work of a rigorous study is justified by the fact that they are inaccessible without it.
An Introduction To Classical Real Analysis
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Author : Karl R. Stromberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-10
An Introduction To Classical Real Analysis written by Karl R. Stromberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-10 with Mathematics categories.
This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf
A Concise Introduction To Analysis
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Author : Daniel W. Stroock
language : en
Publisher: Springer
Release Date : 2015-10-31
A Concise Introduction To Analysis written by Daniel W. Stroock and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-31 with Mathematics categories.
This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
Mathematical Analysis I
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Author : Vladimir A. Zorich
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-22
Mathematical Analysis I written by Vladimir A. Zorich 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 2004-01-22 with Mathematics categories.
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.
Analysis I
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Author : Terence Tao
language : en
Publisher: Springer
Release Date : 2016-08-29
Analysis I written by Terence Tao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-29 with Mathematics categories.
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Real Analysis
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Author : N. L. Carothers
language : en
Publisher: Cambridge University Press
Release Date : 2000-08-15
Real Analysis written by N. L. Carothers 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 2000-08-15 with Mathematics categories.
A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
The Real Analysis Lifesaver
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Author : Raffi Grinberg
language : en
Publisher: Princeton Lifesaver Study Guides
Release Date : 2017
The Real Analysis Lifesaver written by Raffi Grinberg and has been published by Princeton Lifesaver Study Guides this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Functions of real variables categories.
Cover -- Title -- Copyright -- CONTENTS -- Preliminaries -- 1 Introduction -- 2 Basic Math and Logic* -- 3 Set Theory* -- Real Numbers -- 4 Least Upper Bounds* -- 5 The Real Field* -- 6 Complex Numbers and Euclidean Spaces -- Topology -- 7 Bijections -- 8 Countability -- 9 Topological Definitions* -- 10 Closed and Open Sets* -- 11 Compact Sets* -- 12 The Heine-Borel Theorem* -- 13 Perfect and Connected Sets -- Sequences -- 14 Convergence* -- 15 Limits and Subsequences* -- 16 Cauchy and Monotonic Sequences* -- 17 Subsequential Limits -- 18 Special Sequences -- 19 Series* -- 20 Conclusion -- Acknowledgments -- Bibliography -- Index
Real And Functional Analysis
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Real And Functional Analysis written by Serge Lang 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 is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal ysis. I assume that the reader is acquainted with notions of uniform con vergence and the like. In this third edition, I have reorganized the book by covering inte gration before functional analysis. Such a rearrangement fits the way courses are taught in all the places I know of. I have added a number of examples and exercises, as well as some material about integration on the real line (e.g. on Dirac sequence approximation and on Fourier analysis), and some material on functional analysis (e.g. the theory of the Gelfand transform in Chapter XVI). These upgrade previous exercises to sections in the text. In a sense, the subject matter covers the same topics as elementary calculus, viz. linear algebra, differentiation and integration. This time, however, these subjects are treated in a manner suitable for the training of professionals, i.e. people who will use the tools in further investiga tions, be it in mathematics, or physics, or what have you. In the first part, we begin with point set topology, essential for all analysis, and we cover the most important results.