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Preface1 Introduction1 The Set N of Natural Numbers2 The Set Q of Rational Numbers3 fhe Set R of Real Numbers4 The Completeness Axiom5 The Symbols +¡Þ and -¡Þ6 A Development of R 2 Sequences7 Limits of Sequences8 A Discussion about Proofs9 Limit Theorems for Sequences10 Monotone Sequences and Cauchy Sequences11 Subsequences12 limsup's andliminf's13 Some Topological Concepts in Metric Spaces14 Series15 Alternating Series and Integral Tests16 Decimal Expansions of Real Numbers3 Continuity17 Continuous Functions18 Properties of Continuous Functions19 Uniform Continuity20 Limits of Functions21 More on Metric Spaces£ºContinuity22 More on Metric Spaces£ºConnectedness4 Sequences and Series of Functions23 Power Series24 Uniform Convergence25 More on Uniform Convergence26 Differentiation and Integration of Power Series27 Weierstrass's Approximation Theorem5 Differentiation28 Basic Properties of the Derivative29 The Mean Value Theorem30 L'Hospital's Rule31 Taylor's Theorem6 Integration32 The Riemann Integral33 Properties of the Riemann Integral34 Fundamental Theorem of Calculus35 Riemann-Stieltjes Integrals36 Improper Integrals7 Capstone37 A Discussion of Exponents and Logarithms38 Continuous Nowhere¡ªDifferentiable FunctionsAppendix on Set NotationSelected Hints and AnswersA Guide to the ReferencesReferencesSymbols IndexIndex