Index 731Integration, by use of tables,
206-207, 211-212, 465, 474,
514
(See also Integrals)
Interlc4ept form of equation of line,
Intermediate-value theorem, 316,
333
International Business Machine
Corporation (IBM), 47
Interval(s), 5
of convergence, 620
Intrinsic definitions, 48, 585-586
Intrinsic equation of conic, 363, 538
Invariants under rotation, 395
Inverse functions, 458-469
basic theorem for, 459
definition, 458-459
hyperbolic, 507-508
trigonometric, 461-464
Inverse sine, series for, 635
Inverse-square law, 74-75
(See also Gravitational attrac-
tion)
Inverse tangent, series for, 467
Involute of curve, 434
Irrational numbers, 8, 339, 596-
597
Irrationality, of e, 596-597
of square roots, 8
Irreducible polynomial, 448
Isometric transformer, 34
Isothermals, 567
Iterated integrals, 652-667
Iterated limits, 632
Jacobi determinants, 579
Jordan curve theorem, 417
Jump discontinuities, 133
Kepler (planetary motion), 551
Kinetic energy, 187, 257-259, 263Lagrange form of remainder, 634
Lagrange multipliers, 572-573
Laguerre polynomials, 174
Lamina, 270, 667, 676
Laplace equation, 559, 562
Laplace transforms, 686
Laplacian V2u, 582
in cylindrical coordinates, 582
in rectangular coordinates, 582
in spherical coordinates, 582
Lattice points, 32, 152
Law of cosines, 112, 198
Law of mean (see Mean-value
theorem)
Leacock, Stephen, 124
Least integer in set of positive
integers, 320
Least squares, 300
Least upper bound (l.u.b.), 315
Lebesgue integrals, 618, 670, 672
Lebesgue measure, 215, 236, 244,
283, 670, 696, 706
Left-hand continuity, 145
Left-hand derivative, 162
Leibniz notation, 153, 164, 175
Leibniz series for r/4, 468
Lemniscate (of Bernoulli), 389,
532, 533, 538, 549
Length, of circle, 135
of circular arc, 408
of curve, 410
of interval, 5
in polar coordinates, 542
in rectangular coordinates, 417-
423
in spherical coordinates, 710-711
Level surfaces, 566
L'Hopital rules, 330-332
Limacon of Pascal, 538
Limit(s), 122-144
basic theorems on, 127-128,
715-720
for functions of n variables, 557
of integrals, 686