{"product_id":"introduction-to-real-analysis-9780470371367","title":"Introduction to Real Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eAn accessible introduction to real analysis and its connection to elementary calculus\u003c\/b\u003e  \u003cp\u003eBridging the gap between the development and history of real analysis, \u003ci\u003eIntroduction to Real Analysis: An Educational Approach\u003c\/i\u003e presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis.\u003c\/p\u003e \u003cp\u003eThe book begins with an outline of basic calculus, including a close examination of problems illustrating links and potential difficulties. Next, a fluid introduction to real analysis is presented, guiding readers through the basic topology of real numbers, limits, integration, and a series of functions in natural progression. The book moves on to analysis with more rigorous investigations, and the topology of the line is presented along with a discussion of limits and \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003c\/p\u003e\u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Elementary Calculus.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Preliminary Concepts.\u003c\/p\u003e \u003cp\u003e1.2 Limits and Continuity.\u003c\/p\u003e \u003cp\u003e1.3 Differentiation.\u003c\/p\u003e \u003cp\u003e1.4 Integration.\u003c\/p\u003e \u003cp\u003e1.5 Sequences and Series of Constants.\u003c\/p\u003e \u003cp\u003e1.6 Power Series and Taylor Series.\u003c\/p\u003e \u003cp\u003eSummary.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eInterlude: Fermat, Descartes, and theTangent Problem.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Introduction to Real Analysis.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basic Topology of the Real Numbers.\u003c\/p\u003e \u003cp\u003e2.2 Limits and Continuity.\u003c\/p\u003e \u003cp\u003e2.3 Differentiation.\u003c\/p\u003e \u003cp\u003e2.4 Riemann and Riemann-Stieltjes Integration.\u003c\/p\u003e \u003cp\u003e2.5 Sequences, Series, and Convergence Tests.\u003c\/p\u003e \u003cp\u003e2.6 Pointwise and Uniform Convergence.\u003c\/p\u003e \u003cp\u003eSummary.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eInterlude: Euler and the \"Basel Problem\".\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 A Brief Introduction to Lebesgue Theory.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Lebesgue Measure and Measurable Sets.\u003c\/p\u003e \u003cp\u003e3.2 The Lebesgue Integral.\u003c\/p\u003e \u003cp\u003e3.3 Measure, Integral, and Convergence.\u003c\/p\u003e \u003cp\u003e3.4 Littlewood’s Three Principles.\u003c\/p\u003e \u003cp\u003eSummary.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eInterlude: The Set of Rational Numbers isVery Large andVery Small.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Special Topics.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Modeling with Logistic Functions—Numerical Derivatives.\u003c\/p\u003e \u003cp\u003e4.2 Numerical Quadrature.\u003c\/p\u003e \u003cp\u003e4.3 Fourier Series.\u003c\/p\u003e \u003cp\u003e4.4 Special Functions—The Gamma Function.\u003c\/p\u003e \u003cp\u003e4.5 Calculus Without Limits: Differential Algebra.\u003c\/p\u003e \u003cp\u003eSummary.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Definitions and Theorems of Elementary Real Analysis.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Limits.\u003c\/p\u003e \u003cp\u003eA.2 Continuity.\u003c\/p\u003e \u003cp\u003eA.3 The Derivative.\u003c\/p\u003e \u003cp\u003eA.4 Riemann Integration.\u003c\/p\u003e \u003cp\u003eA.5 Riemann-Stieltjes Integration.\u003c\/p\u003e \u003cp\u003eA.6 Sequences and Series of Constants.\u003c\/p\u003e \u003cp\u003eA.7 Sequences and Series of Functions.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B: A Very Brief Calculus Chronology.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C: Projects in Real Analysis.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Historical Writing Projects.\u003c\/p\u003e \u003cp\u003eC.2 Induction Proofs: Summations, Inequalities, and Divisibility.\u003c\/p\u003e \u003cp\u003eC.3 Series Rearrangements.\u003c\/p\u003e \u003cp\u003eC.4 Newton and the Binomial Theorem.\u003c\/p\u003e \u003cp\u003eC.5 Symmetric Sums of Logarithms.\u003c\/p\u003e \u003cp\u003eC.6 Logical Equivalence: Completeness of the Real Numbers.\u003c\/p\u003e \u003cp\u003eC.7 Vitali’s Nonmeasurable Set.\u003c\/p\u003e \u003cp\u003eC.8 Sources for Real Analysis Projects.\u003c\/p\u003e \u003cp\u003eC.9 Sources for Projects for Calculus Students.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBibliography.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402316947799,"sku":"9780470371367","price":95.36,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470371367.jpg?v=1730480048","url":"https:\/\/bookcurl.com\/products\/introduction-to-real-analysis-9780470371367","provider":"Book Curl","version":"1.0","type":"link"}