Introduction to Real Analysis

Introduction to Real Analysis

Helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context.

Author: Robert G. Bartle

Publisher: Wiley

ISBN: 0471433314

Category: Mathematics

Page: 416

View: 733

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.
Categories: Mathematics

Introduction to Real Analysis

Introduction to Real Analysis

I am grateful to the the students of MAT 5930, Analysis for Teachers, for struggling with me while I developed ... W. C. B. CHAPTER 1 ELEMENTARY CALCULUS Introduction We begin our studies by XV Introduction to Real Analysis: An ...

Author: William C. Bauldry

Publisher: John Wiley & Sons

ISBN: 9781118164433

Category: Mathematics

Page: 280

View: 986

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.
Categories: Mathematics

An Introduction to Real Analysis

An Introduction to Real Analysis

AN INTRODUCTION TO REAL ANALYSIS BY DEREK. G. BALL PERG AMON PRESS Oxford . New York . Toronto • Sydney . Braunschweig Pergamon Press Ltd., Headington Hill Hall, Oxford Pergamon Press Inc.,. An Introduction to Real Analysis.

Author: Derek G. Ball

Publisher: Elsevier

ISBN: 9781483158969

Category: Mathematics

Page: 324

View: 118

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.
Categories: Mathematics

Introduction to Real Analysis

Introduction to Real Analysis

The basic topological concepts of open, closed, and compact sets, as well as limits of sequences and functions, are introduced for the real numbers only. However, the proofs of many of the theorems, especially those involving ...

Author: Manfred Stoll

Publisher: Pearson College Division

ISBN: UOM:39015049622288

Category: Mathematics

Page: 550

View: 576

This textbook is designed for a one-year course in real analysis at the junior or senior level. An understanding of real analysis is necessary for the study of advanced topics in mathematics and the physical sciences, and is helpful to advanced students of engineering, economics, and the social sciences. Stoll, who teaches at the U. of South Carolina, presents examples and counterexamples to illustrate topics such as the structure of point sets, limits and continuity, differentiation, and orthogonal functions and Fourier series. The second edition includes a self-contained proof of Lebesgue's theorem and a new appendix on logic and proofs. Annotation copyrighted by Book News Inc., Portland, OR
Categories: Mathematics

Spaces An Introduction to Real Analysis

Spaces  An Introduction to Real Analysis

The text has been tested in classes at the University of Oslo over a number of years.

Author: Tom L. Lindstrøm

Publisher: American Mathematical Soc.

ISBN: 9781470440626

Category: Functional analysis

Page: 369

View: 210

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.
Categories: Functional analysis

Introduction To Real Analysis

Introduction To Real Analysis

An Introduction to Mathematics, 2nd Edition, Universitext, Springer Verlag, 2009. H. Davenport: The Higher Arithmetic ... J. J. Duistermaat, J. A. Kolk: Mutidimensional Real Analysis I. Differentiation, Cambridge University Press, 2004.

Author: Liviu I Nicolaescu

Publisher: World Scientific

ISBN: 9789811210402

Category: Mathematics

Page: 684

View: 288

This is a text that develops calculus 'from scratch', with complete rigorous arguments. Its aim is to introduce the reader not only to the basic facts about calculus but, as importantly, to mathematical reasoning. It covers in great detail calculus of one variable and multivariable calculus. Additionally it offers a basic introduction to the topology of Euclidean space. It is intended to more advanced or highly motivated undergraduates.
Categories: Mathematics

Introduction to Real Analysis

Introduction to Real Analysis

Michael J. Schramm. RE!-\I. ANALYSIS X Michael J. Schramm INTRODUCTION TO REAL ANALYSIS MICHAEL J. SCHRAMM Le Moyne College. INTRODUCTION TO Front Cover.

Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 9780486131924

Category: Mathematics

Page: 384

View: 462

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.
Categories: Mathematics

An Introduction to Real Analysis

An Introduction to Real Analysis

In fact, we provide a compact, but thorough, introduction to the subject in An Introduction to Real Analysis. This book is intended for senior undergraduate and for beginning graduate one-semester courses. Gifted high school students ...

Author: Ravi P. Agarwal

Publisher: CRC Press

ISBN: 9781351180627

Category: Mathematics

Page: 277

View: 873

This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.
Categories: Mathematics

Introduction to Real Analysis

Introduction to Real Analysis

This text is an introduction to real analysis. There are several classic analysis texts that I keep close by on my bookshelf and refer to often. However, I find it difficult to use any of these as the textbook for teaching a first ...

Author: Christopher Heil

Publisher: Springer

ISBN: 9783030269036

Category: Mathematics

Page: 386

View: 326

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.
Categories: Mathematics

A Concrete Introduction to Real Analysis

A Concrete Introduction to Real Analysis

Mathematics 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 ...

Author: Robert Carlson

Publisher: CRC Press

ISBN: 9781420011548

Category: Mathematics

Page: 312

View: 556

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.
Categories: Mathematics