Examples And Theorems In Analysis
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Examples And Theorems In Analysis
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Author : Peter Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Examples And Theorems In Analysis written by Peter Walker 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.
Examples and Theorems in Analysis takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. The results are introduced and motivated by reference to examples which illustrate their use, and further examples then show how far the assumptions may be relaxed before the result fails. A number of applications show what the subject is about and what can be done with it; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems. Written primarily for first- and second-year undergraduates in mathematics, this book features a host of diverse and interesting examples, making it an entertaining and stimulating companion that will also be accessible to students of statistics, computer science and engineering, as well as to professionals in these fields.
Counterexamples In Analysis
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Author : Bernard R. Gelbaum
language : en
Publisher: Courier Corporation
Release Date : 2012-07-12
Counterexamples In Analysis written by Bernard R. Gelbaum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-12 with Mathematics categories.
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.
Examples And Theorems In Analysis
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Author : Peter Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-12
Examples And Theorems In Analysis written by Peter Walker 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 2003-12-12 with Mathematics categories.
This book adopts a practical, example-led approach to mathematical analysis that shows both the usefulness and limitations of the results. A number of applications show what the subject is about and what can be done with it; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems.
Problems And Theorems In Analysis I
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Author : George Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems And Theorems In Analysis I written by George Polya 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.
From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)
Real Analysis
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Author : Halsey Royden
language : en
Publisher:
Release Date : 2018
Real Analysis written by Halsey Royden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Business & Economics categories.
This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.
Basic Real Analysis
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Author : Houshang H. Sohrab
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Basic Real Analysis written by Houshang H. Sohrab 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 2011-06-27 with Mathematics categories.
One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. Basic Real Analysis is a modern, systematic text that presents the fundamentals and touchstone results of the subject in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. Key features include: * A broad view of mathematics throughout the book * Treatment of all concepts for real numbers first, with extensions to metric spaces later, in a separate chapter * Elegant proofs * Excellent choice of topics * Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter * Emphasis on monotone functions throughout * Good development of integration theory * Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis * Solid preparation for deeper study of functional analysis * Chapter on elementary probability * Comprehensive bibliography and index * Solutions manual available to instructors upon request By covering all the basics and developing rigor simultaneously, this introduction to real analysis is ideal for senior undergraduates and beginning graduate students, both as a classroom text or for self-study. With its wide range of topics and its view of real analysis in a larger context, the book will be appropriate for more advanced readers as well.
A Course In Real Analysis
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Author : Hugo D. Junghenn
language : en
Publisher: CRC Press
Release Date : 2015-02-13
A Course In Real Analysis written by Hugo D. Junghenn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-13 with Mathematics categories.
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's two-semester undergraduate course on real analysis at The George Washington University.The first part of the text presents the
Measure Integration Real Analysis
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Author : Sheldon Axler
language : en
Publisher: Springer
Release Date : 2019-12-24
Measure Integration Real Analysis written by Sheldon Axler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Mathematics categories.
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.
Real Analysis
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Author : J. Yeh
language : en
Publisher: World Scientific
Release Date : 2006
Real Analysis written by J. Yeh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.
Basic Elements Of Real Analysis
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Author : Murray H. Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-29
Basic Elements Of Real Analysis written by Murray H. Protter 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 2006-03-29 with Mathematics categories.
From the author of the highly acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one- semester course in real analysis. Many students of mathematics and those students who intend to study any of the physical sciences and computer science need a text that presents the most important material in a brief and elementary fashion. The author has included such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed. There are illustrative examples throughout with over 45 figures.