Fundamentals Of Real Analysis
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Fundamentals Of Real Analysis
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Author : Sterling K. Berberian
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-15
Fundamentals Of Real Analysis written by Sterling K. Berberian 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 2013-03-15 with Mathematics categories.
"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS
Foundations Of Mathematical Analysis
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Author : Richard Johnsonbaugh
language : en
Publisher: Courier Corporation
Release Date : 2012-09-11
Foundations Of Mathematical Analysis written by Richard Johnsonbaugh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
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.
Real Analysis And Foundations
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Author : Steven G. Krantz
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2017
Real Analysis And Foundations written by Steven G. Krantz and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Functions of real variables categories.
The new edition of this popular text is revised to meet the suggestions of users of the previous edition. A readable yet rigorous approach to an essential part of mathematical thinking, this text bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations.
Fundamentals Of Mathematical Analysis
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Author : Adel N. Boules
language : en
Publisher:
Release Date : 2021
Fundamentals Of Mathematical Analysis written by Adel N. Boules and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
"A beginning graduate textbook on real and functional analysis, with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Instructors can choose material from this part as their students' background warrants. Chapter 4 is the spine of the book and is essential for an effective reading of the rest of the book. It is an extensive study of metric spaces, including the core topics of completeness, compactness, and function spaces, with a good number of applications. The remaining chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. The entire book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology, real analysis, or functional analysis. The book is designed as an accessible classical introduction to the subject, aims to achieve excellent breadth and depth, and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity."--Provided by publisher.
The Real Numbers And Real Analysis
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
The Real Numbers And Real Analysis written by Ethan D. Bloch 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 2011-05-27 with Mathematics categories.
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
Fundamentals Of Real Analysis
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Author : James Foran
language : en
Publisher: CRC Press
Release Date : 1991-01-07
Fundamentals Of Real Analysis written by James Foran and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-07 with Mathematics categories.
Guides students from simple aspects of set theory to more complex structures. Based on a two-semester course in real analysis, this textbook explains fundamentals of the theory of functions of a real variable, including subsets of the line, the theory of measure, the Lebesgue integral and its relati
Foundations Of Modern Analysis
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Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 1982-01-01
Foundations Of Modern Analysis written by Avner Friedman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
Modern Real Analysis
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Author : William P. Ziemer
language : en
Publisher: Springer
Release Date : 2018-08-31
Modern Real Analysis written by William P. Ziemer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-31 with Mathematics categories.
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.