LEADER 04113nam 2200589Ia 450 001 9910831196203321 005 20230721010609.0 010 $a1-283-27392-6 010 $a9786613273925 010 $a1-118-16441-5 010 $a1-118-16443-1 035 $a(CKB)2550000000054376 035 $a(EBL)818909 035 $a(OCoLC)757395461 035 $a(SSID)ssj0000554953 035 $a(PQKBManifestationID)11342793 035 $a(PQKBTitleCode)TC0000554953 035 $a(PQKBWorkID)10517636 035 $a(PQKB)10116011 035 $a(MiAaPQ)EBC818909 035 $a(EXLCZ)992550000000054376 100 $a20090331d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to real analysis$b[electronic resource] $ean educational approach /$fWilliam C. Bauldry 210 $aHoboken, N.J. $cWiley$dc2009 215 $a1 online resource (280 p.) 300 $aDescription based upon print version of record. 311 $a0-470-37136-6 320 $aIncludes bibliographical references (p. [253]-257) and index. 327 $aIntroduction 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 327 $a2.6 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 327 $aSummaryExercises; 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 327 $aC.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 330 $aAn 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 606 $aMathematical analysis$vTextbooks 606 $aFunctions$vTextbooks 615 0$aMathematical analysis 615 0$aFunctions 676 $a515 676 $a515.8 700 $aBauldry$b William C$01608047 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910831196203321 996 $aIntroduction to real analysis$93934592 997 $aUNINA