Essential Real Analysis

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Essential Real Analysis

Michael Field
Essential Real Analysis Book PDF

Author : Michael Field
Publisher : Springer
Page : 450 pages
File Size : 45,6 Mb
Release : 2017-11-06
Category : Mathematics
ISBN : 9783319675466

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Essential Real Analysis by Michael Field Pdf

This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

Basic Real Analysis

Houshang H. Sohrab
Basic Real Analysis Book PDF

Author : Houshang H. Sohrab
Publisher : Springer
Page : 683 pages
File Size : 42,8 Mb
Release : 2014-11-15
Category : Mathematics
ISBN : 9781493918416

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Basic Real Analysis by Houshang H. Sohrab Pdf

This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews

Concise Introduction to Basic Real Analysis

Hemen Dutta,P. N. Natarajan,Yeol Je Cho
Concise Introduction to Basic Real Analysis Book PDF

Author : Hemen Dutta,P. N. Natarajan,Yeol Je Cho
Publisher : CRC Press
Page : 188 pages
File Size : 46,6 Mb
Release : 2019-08-12
Category : Mathematics
ISBN : 9780429876332

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Concise Introduction to Basic Real Analysis by Hemen Dutta,P. N. Natarajan,Yeol Je Cho Pdf

This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic. Features Includes basic and essential topics of real analysis Adopts a reasonable approach to make the subject easier to learn Contains many solved examples and exercise at the end of each chapter Presents a quick review of the fundamentals of set theory Covers the real number system Discusses the basic concepts of metric spaces and complete metric spaces

Basic Real Analysis

Anthony W. Knapp
Basic Real Analysis Book PDF

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 47,8 Mb
Release : 2007-10-04
Category : Mathematics
ISBN : 9780817644413

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Basic Real Analysis by Anthony W. Knapp Pdf

Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

Basic Elements of Real Analysis

Murray H. Protter
Basic Elements of Real Analysis Book PDF

Author : Murray H. Protter
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 49,5 Mb
Release : 2006-03-29
Category : Mathematics
ISBN : 9780387227498

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Basic Elements of Real Analysis by Murray H. Protter Pdf

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 the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with 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, backed by illustrative examples throughout and no less than 45 figures.

A Problem Book in Real Analysis

Asuman G. Aksoy,Mohamed A. Khamsi
A Problem Book in Real Analysis Book PDF

Author : Asuman G. Aksoy,Mohamed A. Khamsi
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 48,8 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9781441912961

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A Problem Book in Real Analysis by Asuman G. Aksoy,Mohamed A. Khamsi Pdf

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

A Sequential Introduction to Real Analysis

J M Speight
A Sequential Introduction to Real Analysis Book PDF

Author : J M Speight
Publisher : World Scientific Publishing Company
Page : 276 pages
File Size : 46,5 Mb
Release : 2015-10-29
Category : Mathematics
ISBN : 9781783267859

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A Sequential Introduction to Real Analysis by J M Speight Pdf

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. Request Inspection Copy

Advanced Real Analysis

Anthony W. Knapp
Advanced Real Analysis Book PDF

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 49,5 Mb
Release : 2008-07-11
Category : Mathematics
ISBN : 9780817644420

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Advanced Real Analysis by Anthony W. Knapp Pdf

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

The Real Numbers and Real Analysis

Ethan D. Bloch
The Real Numbers and Real Analysis Book PDF

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 43,9 Mb
Release : 2011-05-27
Category : Mathematics
ISBN : 9780387721767

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The Real Numbers and Real Analysis by Ethan D. Bloch Pdf

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.

Real Analysis and Applications

Fabio Silva Botelho
Real Analysis and Applications Book PDF

Author : Fabio Silva Botelho
Publisher : Springer
Page : 573 pages
File Size : 55,8 Mb
Release : 2018-05-14
Category : Mathematics
ISBN : 9783319786315

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Real Analysis and Applications by Fabio Silva Botelho Pdf

This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

Introduction to Real Analysis

William F. Trench
Introduction to Real Analysis Book PDF

Author : William F. Trench
Publisher : Prentice Hall
Page : 0 pages
File Size : 54,8 Mb
Release : 2003
Category : Applied mathematics
ISBN : 0130457868

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Introduction to Real Analysis by William F. Trench Pdf

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.

Real Analysis (Classic Version)

Halsey Royden,Patrick Fitzpatrick
Real Analysis Classic Version Book PDF

Author : Halsey Royden,Patrick Fitzpatrick
Publisher : Pearson Modern Classics for Advanced Mathematics Series
Page : 0 pages
File Size : 45,5 Mb
Release : 2017-02-13
Category : Functional analysis
ISBN : 0134689496

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Real Analysis (Classic Version) by Halsey Royden,Patrick Fitzpatrick Pdf

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.

Fundamental Mathematical Analysis

Robert Magnus
Fundamental Mathematical Analysis Book PDF

Author : Robert Magnus
Publisher : Springer Nature
Page : 445 pages
File Size : 46,8 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 9783030463212

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Fundamental Mathematical Analysis by Robert Magnus Pdf

This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout. Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.

Real Analysis via Sequences and Series

Charles H.C. Little,Kee L. Teo,Bruce van Brunt
Real Analysis via Sequences and Series Book PDF

Author : Charles H.C. Little,Kee L. Teo,Bruce van Brunt
Publisher : Springer
Page : 476 pages
File Size : 49,5 Mb
Release : 2015-05-28
Category : Mathematics
ISBN : 9781493926510

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Real Analysis via Sequences and Series by Charles H.C. Little,Kee L. Teo,Bruce van Brunt Pdf

This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

Real Analysis

Emmanuele DiBenedetto
Real Analysis Book PDF

Author : Emmanuele DiBenedetto
Publisher : Birkhäuser
Page : 596 pages
File Size : 48,5 Mb
Release : 2016-09-17
Category : Mathematics
ISBN : 9781493940059

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Real Analysis by Emmanuele DiBenedetto Pdf

The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a “Problems and Complements” section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts. The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions. More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions. This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces. Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review. Praise for the First Edition: “[This book] will be extremely useful as a text. There is certainly enough material for a year-long graduate course, but judicious selection would make it possible to use this most appealing book in a one-semester course for well-prepared students.” —Mathematical Reviews