Index 735Riemann-Stieltjes integrals, 261,
276, 353
Right-hand continuity, 145
Right-hand derivative, 162
Right-hand rule, 52
Right-handed system, 60, 66, 73, 99,
103
Rolle theorem, 324
Rollers, triangular, 437
Root test for series, 629
Rose of four leaves, 531
Rosser, John Barkley, 122
Rotation of axes, 107, 394-402
Rounding errors, 281
Ruler and compass constructions,
389,536-538,546
Rules of our game, 1
Saddle surfaces, 407
Sandwich theorem, 128, 719-720
Saw-tooth function, 37, 232, 613,
640
Scalar(s), 43, 49, 177
Scalar acceleration, 44, 180
Scalar (dot) product, 51, 67-77
Scalar triple product, 105
Scalar velocity, 43, 180
Schlicht functions, 459
Schwarz inequality, 78
Schwarz paradox, 448
Secant, series for, 623, 624
Second derivatives, geometric use
of, 304-312
Sector, area of, 440, 476
Semicubical parabola, 413-414
Senatorial secretaries, 300
Sequences, 335, 587, 598-599
Series, 334-342, 587-651
Abel value of, 340
absolutely convergent, 590-592
alternating, 610-611
binomial, 634-635
Cesiro value of, 342
Series, comparison test, 591
convergence value of, 336, 341,
587
converging to, Bernoulli func-
tions, 614
cosine, 458
exponential, 231, 498-499, 505
inverse tangent, 467
log (1 + x)-', 500
7r/4, 468, S00
sine, 458
tangent, 623, 651
definition of, 335, 587
divergent, 336, 587, 588, 603-604
dominated, 591
exponential, 231, 498-499, 505
Fourier, 611-619
geometric, 337-338, 588, 593
harmonic, 594, 644
integral test, 601-603
multiplication of, 623-627
partial sums of, 335, 587
power, 593, 619-640
ratio test, 599-601
rearrangements of, 597-598
root test, 629
2;k-2 = ir2/6, 594, 605, 614, 672
Taylor, 621, 633-636
terms of, 335, 588
termwise addition, 589
termwise differentiation, 620, 632
termwise integration, 620-621,
672
trigonometric, 618-619
uniform convergence, 342
of vectors, 597
Serpentine, 259
Set, bounded, 293
Shell game, 721-723
Signum function, 188, 132, 211, 244
Similarity of parabolas, 360
Simple closed curve, 417
Simple harmonic motion (see Sinus-
oids)