Download or read book Methods of Real Analysis written by Richard R. Goldberg and published by . This book was released on 2019-07-30 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for a one-year course in analysis desighn for students who have completed the ordinary course in elementary calculus.
Download or read book Methods of Real Analysis written by Richard R. Goldberg and published by . This book was released on 1964 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a textbook for a one-year course in analysis desighn for students who have completed the ordinary course in elementary calculus."--Preface.
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 368 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.
Download or read book Introduction to the Methods of Real Analysis written by Maurice Sion and published by New York : Holt, Rinehart and Winston. This book was released on 1968 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pt. I. Topological concepts. 1. Elements of set theory -- 2. Spaces of functions -- 3. Elements of point set topology -- 4. Continuous functions -- pt. II. Measure theory. 5. Measures on abstract spaces -- 6. Lebesgue-Stieltjes measures -- 7. Integration -- 8. Differentiation -- 9. Riesz representation.
Download or read book Real Variable Methods in Harmonic Analysis written by Alberto Torchinsky and published by Elsevier. This book was released on 2016-06-03 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.
Download or read book Essential Real Analysis written by Michael Field and published by Springer. This book was released on 2017-11-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Real Analysis written by Fon-Che Liu and published by Oxford University Press. This book was released on 2016 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. This concise and friendly book is written for early graduate students of mathematics or of related disciplines hoping to learn the basics of Real Analysis with reasonable ease. The essential role of Real Analysis in the construction of basic function spaces necessary for the application of Functional Analysis in many fields of scientific disciplines is demonstrated with due explanations and illuminating examples. After the introductory chapter, a compact but precise treatment of general measure and integration is taken up so that readers have an overall view of the simple structure of the general theory before delving into special measures. The universality of the method of outer measure in the construction of measures is emphasized because it provides a unified way of looking for useful regularity properties of measures. The chapter on functions of real variables sits at the core of the book; it treats in detail properties of functions that are not only basic for understanding the general feature of functions but also relevant for the study of those function spaces which are important when application of functional analytical methods is in question. This is then followed naturally by an introductory chapter on basic principles of Functional Analysis which reveals, together with the last two chapters on the space of p-integrable functions and Fourier integral, the intimate interplay between Functional Analysis and Real Analysis. Applications of many of the topics discussed are included to motivate the readers for further related studies; these contain explorations towards probability theory and partial differential equations.
Download or read book Probabilistic Techniques in Analysis written by Richard F. Bass and published by Springer Science & Business Media. This book was released on 1994-12-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.
Download or read book Introduction to Real Analysis written by William F. Trench and published by Prentice Hall. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Real Analysis written by William C. Bauldry and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Problem Book in Real Analysis written by Asuman G. Aksoy and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 671 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.
Download or read book Real Analysis Classic Version written by Halsey Royden and published by Pearson Modern Classics for Advanced Mathematics Series. This book was released on 2017-02-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Real Analysis Through Modern Infinitesimals written by Nader Vakil and published by Cambridge University Press. This book was released on 2011-02-17 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Download or read book Strange Functions in Real Analysis Second Edition written by A.B. Kharazishvili and published by CRC Press. This book was released on 2000-01-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to explicate extraordinary functions in real analysis and their applications. It examines the Baire category method, the Zermelo-Fraenkel set, the Axiom of Dependent Choices, Cantor and Peano type functions, the Continuum Hypothesis, everywhere differentiable nowhere monotone functions, and Jarnik's nowhere approximately differentiable functions.
Download or read book Problems in Real Analysis written by Teodora-Liliana Radulescu and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
