James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

index A145
hyperbolic function(s), 259
derivatives of, 261
inverse, 261
hyperbolic identities, 260
hyperbolic paraboloid, 836, 837
hyperbolic substitution, 489, 490
hyperboloid, 791, 837
hypersphere, volume of, 1040
hypervolume, 1034
hypocycloid, 648
i (imaginary number), A57
i (standard basis vector), 802
I/D Test, 293
ideal gas law, 236
image of a point, 1053
image of a region, 1053
implicit differentiation, 208, 209, 917, 942
implicit function, 208, 209
Implicit Function Theorem, 942, 943
improper integral, 527
convergence or divergence of, 528, 531
impulse of a force, 464
incompressible velocity field, 1107
increasing function, 19
increasing sequence, 700
Increasing/Decreasing Test, 293
increment, 145, 933
indefinite integral(s), 403
table of, 403
independence of path, 1088
independent random variable, 1022
independent variable, 10, 888, 940
indeterminate difference, 309
indeterminate forms of limits, 304
indeterminate power, 310
indeterminate product, 308
index of summation, A34
inequalities, rules for, A4
inertia (moment of), 1019, 1020,
1036, 1086
infinite discontinuity, 116
infinite interval, 527, 528
infinite limit, 89, 112, 132
infinite sequence. See sequence
infinite series. See series
inflection point, 297
initial condition, 589
initial point
of a parametric curve, 641
of a vector, 798
initial-value problem, 589, 1158
inner product, 807
instantaneous rate of change, 80, 145, 224
instantaneous rate of growth, 229
instantaneous rate of reaction, 227
instantaneous velocity, 81, 143, 224
integer, A2
integrable function, 990
integral(s)
approximations to, 384
change of variables in, 412, 1012, 1052,
1056, 1058, 1059
comparison properties of, 387
conversion to cylindrical
coordinates, 1040
conversion to polar coordinates, 1012
conversion to spherical
coordinates, 1046
definite, 378, 988
derivative of, 394
double (see double integral)
evaluating, 381
improper, 527
indefinite, 402
iterated, 993
line (see line integral)
patterns in, 513
properties of, 385
surface, 1122, 1129
of symmetric functions, 417
table of, 471, 503, 509, rp6–10
triple, 1029, 1030
units for, 408
integral calculus, 2, 3
Integral Test, 721
integrand, 379
discontinuous, 531
integration, 379
approximate, 514
by computer algebra system, 511
of exponential functions, 383, 413
formulas, 471, 503, rp6–10
indefinite, 402
limits of, 379
numerical, 514
partial, 993, 995
by partial fractions, 493
by parts, 472, 473, 474
of a power series, 754
of rational functions, 493
by a rationalizing substitution, 500
reversing order of, 995, 1006
over a solid, 1042
substitution in, 412
tables, use of, 508
term-by-term, 754
of a vector function, 859
intercepts, 315, A19
interest compunded continuously, 241
Intermediate Value Theorem, 123
intermediate variable, 940
interpolation, 27
intersection
of planes, 828
of polar graphs, area of, 670
of sets, A3
of three cylinders, 1044
interval, A3
interval of convergence, 749
inverse cosine function, 64
inverse function(s), 55, 56
inverse sine function, 63
inverse square laws, 36
inverse tangent function, 65
inverse transformation, 1053
inverse trigonometric functions, 63, 64
irrational number, A2
irrotational vector field, 1106
isobar, 895
isothermal, 893
isothermal compressibility, 228
iterated integral, 993
j (standard basis vector), 802
Jacobi, Carl Gustav Jacob, 1055
Jacobian of a transformation, 1055, 1059
jerk, 160
joint density function, 1021, 1036
joule, 455
jump discontinuity, 116
k (standard basis vector), 802
kampyle of Eudoxus, 215
Kepler, Johannes, 686, 875, 880
Kepler’s Laws, 686, 875, 876, 880
kinetic energy, 464, 1093
Kirchhoff’s Laws, 593, 1172
Kondo, Shigeru, 763
Lagrange, Joseph-Louis, 288, 289, 972
Lagrange multiplier, 971, 972
lamina, 562, 1016, 1017
Laplace, Pierre, 920, 1107
Laplace operator, 1107
Laplace’s equation, 920, 1107
lattice point, 274
law of conservation of angular
momentum, 879
Law of Conservation of Energy, 1094
law of cosines, A33
law of gravitation, 460
law of laminar flow, 230, 570
law of natural growth or decay, 237
aw of universal gravitation, 876, 880
laws of exponents, 47, A53, A55
laws of logarithms, 60, A51
learning curve, 591
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.