Index A Abel's Theorem, 234 Absolute convergence, 178 Absolute value, 26 Accumulation point, 39 Additive function, 80,107 continuity of, 106 limits of, 81 Affine function, 107 Algebra: of continuous functions, 86-89 of convergent series, 177 of derivatives, 115-118 of integrable functions, 155-159 of limits of functions, 73-75 of limits of sequences, 43-45 Algebraic number, 26, 29 Alternating series, 187,208 Antiderivative, 155 Approximation: midpoint, 170 trapezoidal, 171 B Bijection, 11 Bijective, 11 Binomial Theorem, 213 Bolzano Intermediate Value Theorem, 100 Bolzano Intermediate Value Theorem, Modified, Bolzano-Weierstrass Theorem, 40 Bound: greatest lower, 22 least upper, 22 lower, 21 upper, 21 Bounded: from above, 21, 36 from below, 21, 36 sequence, 36 set, 21 c Cartesian product, 8 Caratheodory, 134 Cauchy Mean-Value Theorem, 125 Cauchy product, 188-189, 235 Cauchy sequence, 38 Chain rule, 117 Change-of-Variable Theorem, 82,164,168 Closed interval, 24 Closed set, 91 Closure, 96,105 Codomain, 9 Compact set, 92 Comparison test, 179, 207 Complement,relative,5 Complete ordered field, 21 Composition of: continuous functions, 89 differentiable functions, 117 functions, 11, 31 Conditional convergence, 178,186-194 Continuity, uniform, 89 Continuous function, 83 Convergence: absolute, 178 conditional, 178,186-194 interval of, 196 pointwise, 216 radius of, 197-203 sequence of functions, 216 sequence of numbers, 34, 37 series, 173 uniform, 219, 225 Convergent: sequence, 37, 216 237
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