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Record Nr. |
UNINA9910831196203321 |
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Autore |
Bauldry William C |
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Titolo |
Introduction to real analysis [[electronic resource] ] : an educational approach / / William C. Bauldry |
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Pubbl/distr/stampa |
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Hoboken, N.J., : Wiley, c2009 |
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ISBN |
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1-283-27392-6 |
9786613273925 |
1-118-16441-5 |
1-118-16443-1 |
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Descrizione fisica |
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1 online resource (280 p.) |
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Disciplina |
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Soggetti |
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Mathematical analysis |
Functions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [253]-257) and index. |
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Nota di contenuto |
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Introduction to Real Analysis: An Educational Approach; CONTENTS; Preface; Acknowledgments; 1 Elementary Calculus; 1.1 Preliminary Concepts; 1.2 Limits and Continuity; 1.3 Differentiation; 1.4 Integration; 1.5 Sequences and Series of Constants; 1.6 Power Series and Taylor Series; Summary; Exercises; Interlude: Fermat, Descartes, and the Tangent Problem; 2 Introduction to Real Analysis; 2.1 Basic Topology of the Real Numbers; 2.2 Limits and Continuity; 2.3 Differentiation; 2.4 Riemann and Riemann-Stieltjes Integration; 2.5 Sequences, Series, and Convergence Tests |
2.6 Pointwise and Uniform ConvergenceSummary; Exercises; Interlude: Euler and the ""Basel Problem""; 3 A Brief Introduction to Lebesgue Theory; 3.1 Lebesgue Measure and Measurable Sets; 3.2 The Lebesgue Integral; 3.3 Measure, Integral, and Convergence; 3.4 Littlewood's Three Principles; Summary; Exercises; Interlude: The Set of Rational Numbers Is Very Large and Very Small; 4 Special Topics; 4.1 Modeling with Logistic Functions-Numerical Derivatives; 4.2 Numerical Quadrature; 4.3 Fourier Series; 4.4 Special Functions-The Gamma Function; 4.5 Calculus Without Limits: Differential Algebra |
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SummaryExercises; Appendix A: Definitions & Theorems of Elementary Real Analysis; A.1 Limits; A.2 Continuity; A.3 The Derivative; A.4 Riemann Integration; A.5 Riemann-Stieltjes Integration; A.6 Sequences and Series of Constants; A.7 Sequences and Series of Functions; Appendix B: A Brief Calculus Chronology; Appendix C: Projects in Real Analysis; C.1 Historical Writing Projects; C.2 Induction Proofs: Summations, Inequalities, and Divisibility; C.3 Series Rearrangements; C.4 Newton and the Binomial Theorem; C.5 Symmetric Sums of Logarithms |
C.6 Logical Equivalence: Completeness of the Real NumbersC.7 Vitali's Nonmeasurable Set; C.8 Sources for Real Analysis Projects; C.9 Sources for Projects for Calculus Students; Bibliography; Index |
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Sommario/riassunto |
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An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach 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. The book begins with an outline of basic calculus, including a close examination |
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