CONTENTS v
6 Differentiation: Our First View 229
6.1 TheDerivative.............................229
6.1.1 Formulas for Differentiation . . . . . ............242
6.1.2 Revisiting A Geometric Interpretation for the Derivative . . 243
6.2 TheDerivativeandFunctionBehavior................244
6.2.1 Continuity (or Discontinuity) of Derivatives . ........250
6.3 TheDerivativeandFindingLimits..................251
6.4 InverseFunctions...........................254
6.5 DerivativesofHigherOrder .....................258
6.6 Differentiation of Vector-ValuedFunctions..............262
6.7 ProblemSetF.............................266
7Riemann-Stieltjes Integration 275
7.1 RiemannSumsandIntegrability ...................277
7.1.1 Properties of Riemann-StieltjesIntegrals ..........295
7.2 RiemannIntegralsandDifferentiation ................307
7.2.1 Some Methods of Integration . . . . . ............311
7.2.2 The Natural Logarithm Function . . . ............314
7.3 IntegrationofVector-ValuedFunctions................315
7.3.1 Recti¿ableCurves ......................318
7.4 ProblemSetG.............................321
8 Sequences and Series of Functions 325
8.1 PointwiseandUniformConvergence.................326
8.1.1 Sequences of Complex-Valued Functions on Metric Spaces . 334
8.2 Conditions for Uniform Convergence . . . . ............335
8.3 PropertyTransmissionandUniformConvergence..........339
8.4 FamiliesofFunctions.........................349
8.5 TheStone-WeierstrassTheorem ...................363
8.6 ProblemSetH.............................363
9 Some Special Functions 369
9.1 PowerSeriesOvertheReals .....................369
9.2 SomeGeneralConvergenceProperties................379
9.3 DesignerSeries............................388
9.3.1 Another Visit With the Logarithm Function . ........393
9.3.2 A Series Development of Two Trigonometric Functions . . 394
9.4 SeriesfromTaylor’sTheorem ....................397
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2010-01-20
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aphantee2014-05-08这个资料非常好，的确是看鲁丁数分原理的好伴侣。
