A Concrete Introduction to Real Analysis, Second Edition

Author: Robert Carlson

Publisher: CRC Press

ISBN: 1498778143

Category: Mathematics

Page: 298

View: 4235

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The Second Edition offers a major re-organization of the book, with the goal of making it much more competitive as a text for students. The revised edition will be appropriate for a one- or two-semester introductory real analysis course. Like the first edition, the primary audience is the large collection of students who will never take a graduate level analysis course. The choice of topics and level of coverage is suitable for future high school teachers, and for students who will become engineers or other professionals needing a sound working knowledge of undergraduate mathematics.

Introduction to Real Analysis, 4th Edition

Author: Robert G. Bartle,Donald R. Sherbert

Publisher: Wiley Global Education

ISBN: 1118135865

Category: Mathematics

Page: 402

View: 2613

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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, analyze 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 additional 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

Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 0486131920

Category: Mathematics

Page: 384

View: 1809

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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

The Commonwealth and International Library: Mathematical Topics

Author: Derek G. Ball

Publisher: Elsevier

ISBN: 1483158969

Category: Mathematics

Page: 324

View: 6848

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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

Author: William F. Trench

Publisher: Prentice Hall

ISBN: 9780130457868

Category: Mathematics

Page: 574

View: 9991

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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.

Measure and Integral

An Introduction to Real Analysis, Second Edition

Author: Richard L. Wheeden

Publisher: CRC Press

ISBN: 1498702902

Category: Mathematics

Page: 532

View: 4052

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Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content. Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables Includes many new exercises not present in the first edition This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.

Introduction to real analysis

Author: John D. DePree,Charles Swartz

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 355

View: 1056

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Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering. The text presents the first elementary exposition of the gauge integral and offers a clear and thorough introduction to real numbers, developing topics in n-dimensions, and functions of several variables. Detailed treatments of Lagrange multipliers and the Kuhn-Tucker Theorem are also presented. The text concludes with coverage of important topics in abstract analysis, including the Stone-Weierstrass Theorem and the Banach Contraction Principle.

Introduction to Real Analysis

An Educational Approach

Author: William C. Bauldry

Publisher: John Wiley & Sons

ISBN: 1118164431

Category: Mathematics

Page: 280

View: 2665

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An accessible introduction to real analysis and its connectionto elementary calculus Bridging the gap between the development and history of realanalysis, Introduction to Real Analysis: An EducationalApproach presents a comprehensive introduction to real analysiswhile also offering a survey of the field. With its balance ofhistorical background, key calculus methods, and hands-onapplications, this book provides readers with a solid foundationand fundamental understanding of real analysis. The book begins with an outline of basic calculus, including aclose examination of problems illustrating links and potentialdifficulties. Next, a fluid introduction to real analysis ispresented, guiding readers through the basic topology of realnumbers, limits, integration, and a series of functions in naturalprogression. The book moves on to analysis with more rigorousinvestigations, and the topology of the line is presented alongwith a discussion of limits and continuity that includes unusualexamples in order to direct readers' thinking beyond intuitivereasoning and on to more complex understanding. The dichotomy ofpointwise and uniform convergence is then addressed and is followedby differentiation and integration. Riemann-Stieltjes integrals andthe Lebesgue measure are also introduced to broaden the presentedperspective. The book concludes with a collection of advancedtopics that are connected to elementary calculus, such as modelingwith logistic functions, numerical quadrature, Fourier series, andspecial functions. Detailed appendices outline key definitions and theorems inelementary calculus and also present additional proofs, projects,and sets in real analysis. Each chapter references historicalsources on real analysis while also providing proof-orientedexercises and examples that facilitate the development ofcomputational skills. In addition, an extensive bibliographyprovides additional resources on the topic. Introduction to Real Analysis: An Educational Approach isan ideal book for upper- undergraduate and graduate-level realanalysis courses in the areas of mathematics and education. It isalso a valuable reference for educators in the field of appliedmathematics.

Introduction to Real Analysis

Author: Manfred Stoll

Publisher: Addison-Wesley

ISBN: 9780321046253

Category: Mathematics

Page: 550

View: 8124

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This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces. The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives For all readers interested in real analysis.

Analysis 2

Differentialrechnung im Rn, gewöhnliche Differentialgleichungen

Author: Otto Forster

Publisher: Springer-Verlag

ISBN: 3322919080

Category: Mathematics

Page: 164

View: 1364

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Der vorliegende Band stellt den zweiten Teil eines Analysis-Kurses für Studierende der Mathematik und Physik dar. Das erste Kapitel über Differentialrechnung im R^n behandelt nach einer Einführung in die topologischen Grundbegriffe Kurven im R^n, partielle Ableitungen, totale Differenzierbarkeit, Taylorsche Formel, Maxima und Minima von Funktionen mehrerer Veränderlichen, implizite Funktionen und parameterabhängige Integrale. Das zweite Kapitel gibt eine kurze Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Nach dem Beweis des allgemeinen Existenz- und Eindeutigkeitssatzes und der Besprechung der Methode der Trennung der Variablen wird besonders auf die Theorie der linearen Differentialgleichungen eingegangen.

A Sequential Introduction to Real Analysis

Author: J M Speight

Publisher: World Scientific Publishing Company

ISBN: 1783267852

Category: Mathematics

Page: 276

View: 6985

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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

Basic Analysis I

Introduction to Real Analysis

Author: Jiri Lebl

Publisher: Createspace Independent Publishing Platform

ISBN: 9781718862401

Category:

Page: 282

View: 2228

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Version 5.0. A first course in rigorous mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison and Math 4143 at Oklahoma State University. The first volume is either a stand-alone one-semester course or the first semester of a year-long course together with the second volume. It can be used anywhere from a semester early introduction to analysis for undergraduates (especially chapters 1-5) to a year-long course for advanced undergraduates and masters-level students. See http://www.jirka.org/ra/ Table of Contents (of this volume I): Introduction 1. Real Numbers 2. Sequences and Series 3. Continuous Functions 4. The Derivative 5. The Riemann Integral 6. Sequences of Functions 7. Metric Spaces This first volume contains what used to be the entire book "Basic Analysis" before edition 5, that is chapters 1-7. Second volume contains chapters on multidimensional differential and integral calculus and further topics on approximation of functions.

INTRODUCTION TO REAL ANALYSIS, 3RD ED

Author: Bartle

Publisher: John Wiley & Sons

ISBN: 9788126511099

Category:

Page: 400

View: 423

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Market_Desc: · Mathematicians Special Features: · The book present results that are general enough to cover cases that actually arise, but do not strive for maximum generality· It also present proofs that can readily be adapted to a more general situation· It contains a rather extensive lists of exercises, some difficult for the more challenged. Moderately difficult exercises are broken down into a sequence of steps About The Book: In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this text provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

Introduction to Real Analysis

Author: S.K. Mapa

Publisher: Sarat Book Distributors

ISBN: 9788187169024

Category:

Page: 662

View: 4674

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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

Author: V. K. Bhat

Publisher: Alpha Science International Limited

ISBN: 9781842657058

Category: Mathematics

Page: 228

View: 810

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AN INTRODUCTION TO REAL ANALYSIS covers some basic results pertaining to the set of real numbers. It is a foundational course for beginners. It includes chapters like real number system, sequences, limit and continuity of functions, differentiability and integration. A chapter on inequalities supplements other chapters. Each chapter contains some examples and an exercise set. Solving these exercises will make the subject interesting. Pre requistte for this book is the basic knowledge of real numbers.