Smith R., Minton R. Calculus
Подождите немного. Документ загружается.
P1: NAI/NAI P2: NAI/NAI QC: NAI/NAI T1: NAI
MHDQ256-Sub-Index MHDQ256-Smith-v1.cls January 10, 2011 11:25
LT (Late Transcendental)
CONFIRMING PAGES
Subject Index I-17
Terminal point, of vector, 688
Terminal velocity, 361, 509
Tetrahedron, triple integral over,
940–941
Thermal diffusivity, 862
Third derivatives, 131
Three body problems, 184
Three-dimensions, plotting points in,
698
Three-leaf rose, 661
Threshold, critical, 512
Thrust-time curve, 370
Timbre, 617
Time, doubling, 493
TNB frame, 788
Topographical map, 821
Torque, 721, 722, 775
Torsion, 798
Total area, defined, 275
Total differential, 850
Transform, Laplace, 478
Transformation
changing variables for, 968
image of, 963
in polar coordinates, 965
Jacobian of, 967
linear, 27
direct, 972
of data, 9
of functions, 36–41
combination, 36
composition, 36
finding, 37
identification of, 37
stretching, 40
of simple region, 964
one-to-one, 963
Transient solution, 1086
Translation(s)
comparing, 39
horizontal, 38–39
vertical, 37–38
Trapezoidal Rule, 302, 304
Triangle Inequality, 708, 712
Triangle inequality, 5
Triangular wave function, Fourier series
expansion, 611–612
Trigonometric functions, 26–34
derivatives of, 147–152
in powers, 294
integrals involving powers of,
433–437
inverse, 399–403
calculus of, 405–409
derivatives of, 406
integrals involving, 407–409
simplification of, 402
limit of, 63, 80, 91
loss of significance involving, 101
polynomial and, sum of, 220–221
Trigonometric identities, 32
Trigonometric substitution, 437–440,
448
Trihedral, moving, 788
Triple integrals, 928–946
center of mass and, 944–946
change of variables in, 970
defined, 928
for volume, 952–953
in cylindrical coordinates, 950–951
in spherical coordinates, 957–960
inner partition of, 929
order of integration in, 942–943
over rectangular box, 929
over tetrahedron, 940–941
volume with, 943–944
with first integration with respect
to x, 941–942
with polar coordinates, 948
Trochoid, 640
Trojan asteroids, 185
Two-sided inequality, 3–4
Two-sided surface, 1039
U
Undamped pendulum, 1094
Undetermined coefficients, method of,
1083
Unit ball, 957
Unit normal vector
principal, 786
Unit tangent vector, 780, 787–788
Unit vector, 693, 701
Universal law of gravitation, 680, 794
Unstable equilibrium solutions, 512,
522
Up concavity, 203
Upper limit of integration, 273
Useful life phase, 421
V
Variable(s)
change of
in antiderivative, 968–969
in double integral, 967
in multiple integrals, 962–971
in triple integral, 970
dimensionless, 858
several, functions of, 809–818
extrema of, 874–883
two, functions of, 809–810
Vector field(s), 977–987
conservative, 1003–1011
definition of, 1009
determination of, 1010, 1027
curl of, 1022–1029
computing, 1023
definition of, 1023
interpretation of, 1024
definition of, 978
divergence of, 1022–1029
computing, 1025
definition of, 1025
flux of, 1039–1041
graphing of, 978–979
incompressible, 1026
irrotational, 1024, 1027–1028
plotting, 978
potential function of, 1010
sink points, 1026
source points, 1026
source-free, 1026
with gradient, 1026
Vector format, 627
Vector-valued curves
graph of, 750–751
orientation of, 751
Vector-valued functions
antiderivative of, 765
calculus of, 758–767
continuity of, 759–760
defined, 750
definite integral of, 766
derivative of, 761
differentiation of, 761
ellipse, 751
elliptical helix, 751–752
graphing of, 750–751
increment of, 760
indefinite integral of, 766
limit of, 759
line, 752
matching to graph, 752
Vector(s)
acceleration, 770
addition of, 688–689
additive inverse of, 691, 700
angle between two, 706
arithmetic with, 690–691
binormal, 788
components of, 689, 708–711
cross product, 714–723
direction, 711
displacement, 710
dot product of, 704–711
first component of, 689
horizontal component of, 637, 693
in plane, 688–695
P1: NAI/NAI P2: NAI/NAI QC: NAI/NAI T1: NAI
MHDQ256-Sub-Index MHDQ256-Smith-v1.cls January 10, 2011 11:25
LT (Late Transcendental)
CONFIRMING PAGES
I-18 Subject Index
Vector(s)—Cont.
in R
3
, 699–702
in space, 697–702
initial point of, 688
magnitude of, 688, 700
normal, 712, 728, 786–797
normalization of, 693
notation, 688
opposite, 690
orthogonal, 706, 792
parallel, 691
perpendicular, 706
polar form of, 694
position, 689, 692, 750
price, 713
principal unit normal, 786
projection of, 708–711
orthogonal, 712
resultant, 688
right-handed coordinate system and,
697
sales, 713
scalar product of, 705
scalar triple product of, 721
scalars and, 688
second component of, 689
standard basis, 693
subtraction of, 689
tangent, 764, 786–797
terminal point of, 688
unit, 693, 701
unit tangent, 780, 787–788
velocity, 770
vertical component of, 693
zero, 691, 700
Velocity
angular, 774
average, 112–113
escape, 86
estimating numerically, 124
from acceleration, 770
from position, 770
horizontal component of, 637
instantaneous, 113
limit describing, 66
tangent lines and, 107–115
terminal, 361, 509
vector, 770
vertical component of, 637
Velocity field, 981
flux of, 1061–1062
Verhulst, Pierre, 505
Vertex
of ellipse, 671
Vertical asymptotes, 24
in graphing, 212, 215–216
Vertical component, of vector, 637
Vertical line test, 13
Vertical translation(s), 37–38
Volume
beneath surface, 904–905
between two paraboloids, 930
calculation of
by cross-sectional areas, 326–327
by cylindrical shells, 338–343
by slicing, 325–328
by washers, 330–335, 340
disk method for, 328–330
estimating
from cross-sectional data, 327
in polar coordinates, 928
in spherical coordinates, 959–960
maximization of, 224–225
of cylinder, 325, 665
of dome, 328
of parallelepiped, 721
of solid, 331–332, 919
of solid with cavities, 331–332
rate of change of, 157
with double integrals, 918
with triple integrals, 943–944,
952–953
W
Washers, method of, 330–335,
340
Watts, Robert, 357
Wave equation, 843
Wave function, 1098
Weierstrass M-test, 586
Weierstrass, Karl, 74
Weight density, 947
Well-defined functions, 290
Wiles, Andrew, 189
Witten, Edward, 790
Work
calculation of, 362, 710
defined, 361
line integrals and, 999–1000
Y
Yau, Shing-Tung, 837
Yoccoz, Jean-Christophe, 455
Z
Zero of multiplicity, 68, 184, 466
Zero vector, 691, 700
Zero(s) of function
approximate, 25
approximating
by method of bisection, 74–75
by Newton’s method, 179
Bessel function, 603
by factoring, 16
by quadratic formula, 16
cubic polynomial, 17
determining number of, 164
finding, by method of bisections,
74–75