A Course In Real Analysis

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A Course in Real Analysis

Author : John N. McDonald
Publisher : Academic Press
ISBN 13 : 9780123877741
Total Pages : 0 pages
Book Rating : 4.8/5 (777 download)

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Book Synopsis A Course in Real Analysis by : John N. McDonald

Download or read book A Course in Real Analysis written by John N. McDonald and published by Academic Press. This book was released on 2012-01-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.

A Course in Real Analysis

Author : Hugo D. Junghenn
Publisher : CRC Press
ISBN 13 : 148221928X
Total Pages : 613 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A Course in Real Analysis by : Hugo D. Junghenn

Download or read book A Course in Real Analysis written by Hugo D. Junghenn and published by CRC Press. This book was released on 2015-02-13 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

A First Course in Real Analysis

Author : M.H. Protter
Publisher : Springer Science & Business Media
ISBN 13 : 1461599903
Total Pages : 520 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis A First Course in Real Analysis by : M.H. Protter

Download or read book A First Course in Real Analysis written by M.H. Protter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.

A First Course in Real Analysis

Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
ISBN 13 : 1441985484
Total Pages : 249 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A First Course in Real Analysis by : Sterling K. Berberian

Download or read book A First Course in Real Analysis written by Sterling K. Berberian and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

A Basic Course in Real Analysis

Author : Ajit Kumar
Publisher : CRC Press
ISBN 13 : 1482216388
Total Pages : 322 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A Basic Course in Real Analysis by : Ajit Kumar

Download or read book A Basic Course in Real Analysis written by Ajit Kumar and published by CRC Press. This book was released on 2014-01-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis. Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.

Introduction to Analysis

Author : Edward Gaughan
Publisher : American Mathematical Soc.
ISBN 13 : 0821847872
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Analysis by : Edward Gaughan

Download or read book Introduction to Analysis written by Edward Gaughan and published by American Mathematical Soc.. This book was released on 2009 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section."--pub. desc.

Real Analysis

Author : N. L. Carothers
Publisher : Cambridge University Press
ISBN 13 : 9780521497565
Total Pages : 420 pages
Book Rating : 4.4/5 (975 download)

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Book Synopsis Real Analysis by : N. L. Carothers

Download or read book Real Analysis written by N. L. Carothers and published by Cambridge University Press. This book was released on 2000-08-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

Real Mathematical Analysis

Author : Charles Chapman Pugh
Publisher : Springer Science & Business Media
ISBN 13 : 0387216847
Total Pages : 445 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Real Mathematical Analysis by : Charles Chapman Pugh

Download or read book Real Mathematical Analysis written by Charles Chapman Pugh and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Real Analysis: A Comprehensive Course in Analysis, Part 1

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470410990
Total Pages : 789 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Real Analysis: A Comprehensive Course in Analysis, Part 1 by : Barry Simon

Download or read book Real Analysis: A Comprehensive Course in Analysis, Part 1 written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Basic Real Analysis

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
ISBN 13 : 0817644415
Total Pages : 656 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Basic Real Analysis by : Anthony W. Knapp

Download or read book Basic Real Analysis written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Real Analysis

Author : Gerald B. Folland
Publisher : John Wiley & Sons
ISBN 13 : 1118626397
Total Pages : 309 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Real Analysis by : Gerald B. Folland

Download or read book Real Analysis written by Gerald B. Folland and published by John Wiley & Sons. This book was released on 2013-06-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.

Real Analysis via Sequences and Series

Author : Charles H.C. Little
Publisher : Springer
ISBN 13 : 1493926519
Total Pages : 476 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Real Analysis via Sequences and Series by : Charles H.C. Little

Download or read book Real Analysis via Sequences and Series written by Charles H.C. Little and published by Springer. This book was released on 2015-05-28 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Book of Abstract Algebra

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486474178
Total Pages : 402 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Abstract Algebra by : Charles C Pinter

Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Elements of Real Analysis

Author : David A. Sprecher
Publisher : Courier Corporation
ISBN 13 : 0486153258
Total Pages : 357 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Elements of Real Analysis by : David A. Sprecher

Download or read book Elements of Real Analysis written by David A. Sprecher and published by Courier Corporation. This book was released on 2012-04-25 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.

Real Analysis

Author : Frank Morgan
Publisher : American Mathematical Soc.
ISBN 13 : 0821836706
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Real Analysis by : Frank Morgan

Download or read book Real Analysis written by Frank Morgan and published by American Mathematical Soc.. This book was released on 2005 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as ``closed and bounded,'' via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. The text not only provides efficient proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a real analysis text that is short enough for the student to read and understand and complete enough to be the primary text for a serious undergraduate course. Frank Morgan is the author of five books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this book, Morgan has finally brought his famous direct style to an undergraduate real analysis text.

A Course in Calculus and Real Analysis

Author : Sudhir R. Ghorpade
Publisher : Springer Science & Business Media
ISBN 13 : 0387305300
Total Pages : 442 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis A Course in Calculus and Real Analysis by : Sudhir R. Ghorpade

Download or read book A Course in Calculus and Real Analysis written by Sudhir R. Ghorpade and published by Springer Science & Business Media. This book was released on 2006-06-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

Elements of Real Analysis

Author : M.A. Al-Gwaiz
Publisher : CRC Press
ISBN 13 : 142001160X
Total Pages : 436 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Elements of Real Analysis by : M.A. Al-Gwaiz

Download or read book Elements of Real Analysis written by M.A. Al-Gwaiz and published by CRC Press. This book was released on 2006-08-21 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.