Introduction To Real Analysis
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An Introduction To Real Analysis
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Author : Derek G. Ball
language : en
Publisher: Elsevier
Release Date : 2014-05-17
An Introduction To Real Analysis written by Derek G. Ball and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-17 with Mathematics categories.
An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.
Introduction To Real Analysis
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Author : Robert G. Bartle
language : en
Publisher: Wiley
Release Date : 2011-01-18
Introduction To Real Analysis written by Robert G. Bartle and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-18 with Mathematics categories.
"This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible"--
Introduction To Real Analysis
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Author : William F. Trench
language : en
Publisher: Prentice Hall
Release Date : 2003
Introduction To Real Analysis written by William F. Trench and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Applied mathematics categories.
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
Introduction To Real Analysis
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Author : Michael J. Schramm
language : en
Publisher: Courier Corporation
Release Date : 2008-11-24
Introduction To Real Analysis written by Michael J. Schramm and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-24 with Mathematics categories.
This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
A Sequential Introduction To Real Analysis
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Author : J Martin Speight
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-10-29
A Sequential Introduction To Real Analysis written by J Martin Speight and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-29 with Mathematics categories.
Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.
Introduction To Real Analysis
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Author : S.K. Mapa
language : en
Publisher: Sarat Book Distributors
Release Date : 2014-04
Introduction To Real Analysis written by S.K. Mapa and has been published by Sarat Book Distributors this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04 with Mathematics categories.
This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
An Introduction To Real Analysis
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Author : Yitzhak Katznelson
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-22
An Introduction To Real Analysis written by Yitzhak Katznelson and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-22 with Mathematics categories.
An Introduction to Real Analysis gives students of mathematics and related sciences an introduction to the foundations of calculus, and more generally, to the analytic way of thinking. The authors' style is a mix of formal and informal, with the intent of illustrating the practice of analysis and emphasizing the process as much as the outcome. The book is intended for use in a one- or two-term course for advanced undergraduates in mathematics and related fields who have completed two or three terms of a standard university calculus sequence.
A Concrete Introduction To Real Analysis
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Author : Robert Carlson
language : en
Publisher: CRC Press
Release Date : 2006-05-30
A Concrete Introduction To Real Analysis written by Robert Carlson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-30 with Mathematics categories.
Most volumes in analysis plunge students into a challenging new mathematical environment, replete with axioms, powerful abstractions, and an overriding emphasis on formal proofs. This can lead even students with a solid mathematical aptitude to often feel bewildered and discouraged by the theoretical treatment. Avoiding unnecessary abstractions to provide an accessible presentation of the material, A Concrete Introduction to Real Analysis supplies the crucial transition from a calculations-focused treatment of mathematics to a proof-centered approach. Drawing from the history of mathematics and practical applications, this volume uses problems emerging from calculus to introduce themes of estimation, approximation, and convergence. The book covers discrete calculus, selected area computations, Taylor's theorem, infinite sequences and series, limits, continuity and differentiability of functions, the Riemann integral, and much more. It contains a large collection of examples and exercises, ranging from simple problems that allow students to check their understanding of the concepts to challenging problems that develop new material. Providing a solid foundation in analysis, A Concrete Introduction to Real Analysis demonstrates that the mathematical treatments described in the text will be valuable both for students planning to study more analysis and for those who are less inclined to take another analysis class.
Introductory Real Analysis
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Author : A. N. Kolmogorov
language : en
Publisher: Courier Corporation
Release Date : 1975-06-01
Introductory Real Analysis written by A. N. Kolmogorov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-06-01 with Mathematics categories.
Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.
Introduction To Real Analysis
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Author : Manfred Stoll
language : en
Publisher: CRC Press
Release Date : 2021-03-09
Introduction To Real Analysis written by Manfred Stoll and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-09 with Mathematics categories.
This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition. This text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course, taking into consideration the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student, w hile at the same time challenging the more talented student through the exercises. Chapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters, the theorems, examples, and exercises require greater sophistication and mathematical maturity for full understanding. In addition to the standard topics the text includes topics that are not always included in comparable texts. Chapter 6 contains a section on the Riemann-Stieltjes integral and a proof of Lebesgue’s t heorem providing necessary and sufficient conditions for Riemann integrability. Chapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces. C hapter 8 contains a proof of the Weierstrass approximation theorem using the method of aapproximate identities. The inclusion of Fourier series in the text allows the student to gain some exposure to this important subject. The final chapter includes a detailed treatment of Lebesgue measure and the Lebesgue integral, using inner and outer measure. The exercises at the end of each section reinforce the concepts. Notes provide historical comments or discuss additional topics.