726 Index
Closed curve, 416 Convexity of curves, 305
Closed interval a < x S b, 5 Coordinates, on curve, 421
Commutative operations, 556 cylindrical, 527
Comparison test for convergence, on line, 2
591 in plane, 10
Complete orthonormal sets, 613 polar, 528-552
Completeness of real numbers, 313 rectangular, 10, 59
Completion of squares, 26 in space, 59, 101
Complex exponentials, 628, 651 spherical, 527
Complex numbers, 139, 505-506, Corn-popper function, 151-152,
516-517,628^220
Components, of plane sets, 417 Corners, 293
troublesome word, 61 Correlation, 77
of vectors, 61, 179 Cosine, power series for, 458
Composite functions, 165 Cosmology, 606, 711-714
Composite integers, 120 Coulomb law, 255
Computers, 121, 280, 282, 340, Countable collection, 216, 236
453, 458, 468, 486, 512 Critical values (derivative zero),
Concave,305^295
Conchoid of Nicomedes, 536 Cross products (see Vector
Cones, 64, 76, 361, 369, 570 products)
volume of solid, 245-246 Curl (of vector), 561, 673
Cones and conics, 361-407 Curly dees, 554
Confocal conics, 387 Curvature, 432-433
Confocal ellipses, 378 in polar coordinates, 535
Conics, 361-407, 539, 551 Curve(s), 150, 177-179, 408-437,
in polar coordinates, 539^540
Conjugate hyperbolas, 382 closed, 416
Connected set, 416 having finite length, 410
Connecting rod, 191 having infinite length, 416
Conservation of energy, 187 in polar coordinates, 538-552
Conservative force fields, 657- simple, 417
658, 675 on spheres, 184-185
Constants, 15 on torus, 186
of integration, 204 Curve integrals, 426-428, 673-676
Continuity, 144 independent of path, 658, 676
basic theorems on, 314-317, 326 Cusp, 414
over closed interval, 146 Cyclic advance of subscripts, 21
of functions of n variables, 557 Cycloids, 311, 399-400, 422, 435
uniform, 326 Cylinders, 83, 403
unilateral, 145 Cylindrical coordinates, 527, 532-
Convergence, of sequences, 335 533, 582, 703-707
of series, 336, 587 triple integrals in, 702-707
Convex sets, 293, 551 Cylindrical shell method, 246