Preface 1 Introduction 1 TheSet N of Natural Numbers 2 The Set Q of Rational Numbers 3 The Set R of Real Numbers 4 The Completeness Axiom 5 The Symbols +oo and -oo 6 * A Development of R 2 Sequences 7 Limits of Sequences 8 A Discussion.about Proofs 9 Limit Theorems for Sequences 10 Monotone Sequences and Cauchy Sequences 11 Subsequences 12 lim sap's and lim inf's 13 * Some Topological Concepts in Metric spaces 14 Series 15 Aternatin4g Series and Integral Tests 16 * Decimal Expansions of Real Numbers 3 Continuity 17 Continuous Functions 18 Properties of Continuous Functions 19 Uniform Continuity 20 Limits of Functions 21 * More on Metric Spaces: Continuity 22 * More on Metric Spaces: Connectedness 4 Sequences and Series of Functions 23 Power Series 24 Uniform Convergence 25 More on Uniform Convergence 26 Differentiation and Integration of Power series 27 * weierstrass's Approximation Theorem 5 Differentiation 28 Basic Properties of the Derivative 29 The Mean Value Theorem 30 * UHospital's Rule 31 Taylor s Theorem 6 Integration 32 The Riemann Integral 33 Properties of the Riemann Integral 34 Fundamental Theorem of Calctflus 35 * Riemann-Stieltjes Integrals 36 * Improper Integrals 37 * A Discussion of Exponents and Logarithms Appendix on Set Notation Selected Hints and Answers References Symbols Index Index
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