INDEX 0 451
Moments, by integration, 31.24 to
31.32, 44.80 to 44.85, 44.89
to 44.92
Moments of inertia, 44.86 to 44.88
Motion:
curvilinear, 34.43 to 34.108
rectilinear, 17.1 to 17.35, 19.34
to 19.39, 19.41, 19.44, 19.57,
19.59, 19.72 to 19.76
Multiple integrals:
area with, 44.20, 44.36 to 44.38
centroids (center of mass) with,
44.80 to 44.85, 44.89 to
44.92
double integrals, 44.1 to 44.4,
44.6 to 44.46, 44.53 to 44.58,
44.74, 44.75, 44.79 to 44.82,
44.86, 44.87, 44.89, 44.90
iterated integrals, 44.1 to 44.5
mass with, 44.74 to 44.79
moments of inertia with, 44.86 to
44.88
moments with, 44.80 to 44.85,
44.89 to 44.92
surface area with, 44.53 to 44.58
triple integrals, 44.5, 44.50 to
44.52, 44.59 to 44.73, 44.76
to 44.78, 44.83 to 44.85,
44.88, 44.91,44.92
volume with, 44.16 to 44.19,
44.21 to 44.23, 44.29 to
44.32,44.34,44.40,44.41,
44.50, 44.51, 44.59 to 44.63,
44.66 to 44.70
Multivariate functions, 41.1 to 41.66
Natural logarithms:
antiderivatives (indefinite
integrals) and, 23.10 to
23.22, 23.53, 23.68, 23.69,
23.79,23.80,28.7,28.16,
28.19,28.22, 28.24, 28.55 to
28.57
approximations for, 38.52, 38.53,
39.28, 39.40
defined, 23.1
definite integrals and, 23.36 to
23.38, 23.56, 23.57, 23.59,
23.61,23.63,23.73, 28.25 to
28.31, 32.4, 32.5, 32.8,
32.10, 32.15,32.16, 32.36,
32.37, 32.50
derivatives of, 23.1 to 23.9
graphs of, 23.39, 23.40, 23.46,
23.47, 23.55, 23.76, 25.54,
25.55
inequalities for, 23.41, 23.42,
23.60, 23.77
limits and, 22.43 to 22.45, 23.52,
23.71,23.72
Natural logarithms (Con?.):
Maclaurin series and, 39.5,
39.20, 39.28, 39.34, 39.40,
39.46, 39.50
power series and, 38.38, 38.50 to
38.53, 38.60, 38.86, 38.88,
38.94, 38.99,38.100
properties of, 23.27 to 23.34,
23.64,24.1 to 24.6, 24.35,
24.65 to 24.71
Simpson's rule approximations
for, 23.73
Taylor series and, 39.6
trapezoidal rule approximations
for, 23.57
(See also Exponential functions)
Newton's law of cooling, 26.22,
26.39
Newton's second law of motion,
19.95, 19.%
Normal acceleration, 34.106 to
34.108
Normal distribution:
approximations for, 38.46, 39.41
power series for, 38.45
Normal lines, 8.16, 8.19,8.33,
8.36,8.37,9.14,9.19, 10.23,
10.28, 34.27,42.117
Normal planes, 42.120, 42.121,
45.3, 45.4, 45.6
Normal vectors, 42.105 to 42.115,
42.122 to 42.126, 45.19
Odd functions, 5.43, 5.44, 5.46, 5.49,
5.51,5.52, 5.54 to 5.56, 5.90
to 5.92, 8.46, 8.47, 15.34,
15.47, 15.51,20.48,20.49,
24.97, 38.74, 38.93
One-one functions, 5.57, 5.58,
5.60, 5.63, 5.69 to 5.74,
5.92, 5.93, 5.100, 9.49
One-sided limits, 6.5, 6.33 to 6.36,
6.39
Orthogonal trajectories, 46.22 to
46.24
Osculating planes, 45.18 to 45.20
p-series, 37.40, 37.44, 37.47, 37.54,
37.69, 37.74, 37.78, 37.82,
37.85, 37.88, 37.89, 37.95,
38.11, 38.21
Pappus's theorem for volume,
31.33 to 31.35
Parabolas:
as contours (level curves), 41.35,
41.38, 41.42
curvature (K) of, 34.98
graphs of, 5.1,5.2, 5.11,5.101,
8.44, 15.30, 16.2, 16.47,
34.3, 34.4,34.7,35.15,41.19
Parabolas (Cont.):
intersections of lines with, 3.80
intersections of, 12.45
latus rectum of, 44.80
parametric equations of, 34.3,
34.4, 34.7
in polar coordinates, 35.15
tangents to, 8.28
vertex of, 15.30, 21.13,21.15,
21.22,21.23
Paraboloids:
equations for, 41.80
graphs of, 41.4, 41.5, 41.9, 41.17,
41.25
as ruled surfaces, 41.30
Parallel lines, 3.12 to 3.15, 3.23,
3.24, 3.66, 3.68, 8.23, 40.72
to 40.74
Parallel planes, 40.90, 40.91
Parallel vectors, 33.4, 33.5, 33.36,
33.39, 40.68
Parallelepipeds, 40.45, 40.49,
40.56, 40.63
Parallelogram law for vectors,
33.17
Parallelograms:
area of, 40.43, 40.110,40.111
diagonals of, 33.26, 33.30
quadrilaterals and, 3.42
rhombuses as, 3.76
vertices of, 3.28, 40.109
Parametric equations, 34.1 to
34.42, 40.69 to 40.79,
40.85
Partial derivatives, 42.1 to 42.126
Partial differential equations:
Cauchy-Riemann equations,
42.54, 42.92
Laplace's equation, 42.52 to
42.54
wave equation, 42.55 to 42.58
Partial fractions, 30.1 to 30.33,
46.22
Partial sums, 37.4, 37.5, 37.10,
37.17 to 37.22, 37.24,37.25
Perimeter:
circle, 16.46
rectangle, 16.1, 16.15, 16.29,
16.35, 16.41, 16.44, 16.46,
16.60
triangle, 16.19, 16.20, 16.55,
16.60, 16.61
Period of trigonometric functions,
10.12, 10.13, 10.45
Perpendicular bisectors, 3.35,
3.74
Perpendicular lines, 3.20 to 3.23,
3.25, 3.26, 3.31, 3.69, 40.75,
40.77
Perpendicular planes, 40.95
Moments, by integration, 31.24 to
31.32, 44.80 to 44.85, 44.89
to 44.92
Moments of inertia, 44.86 to 44.88
Motion:
curvilinear, 34.43 to 34.108
rectilinear, 17.1 to 17.35, 19.34
to 19.39, 19.41, 19.44, 19.57,
19.59, 19.72 to 19.76
Multiple integrals:
area with, 44.20, 44.36 to 44.38
centroids (center of mass) with,
44.80 to 44.85, 44.89 to
44.92
double integrals, 44.1 to 44.4,
44.6 to 44.46, 44.53 to 44.58,
44.74, 44.75, 44.79 to 44.82,
44.86, 44.87, 44.89, 44.90
iterated integrals, 44.1 to 44.5
mass with, 44.74 to 44.79
moments of inertia with, 44.86 to
44.88
moments with, 44.80 to 44.85,
44.89 to 44.92
surface area with, 44.53 to 44.58
triple integrals, 44.5, 44.50 to
44.52, 44.59 to 44.73, 44.76
to 44.78, 44.83 to 44.85,
44.88, 44.91,44.92
volume with, 44.16 to 44.19,
44.21 to 44.23, 44.29 to
44.32,44.34,44.40,44.41,
44.50, 44.51, 44.59 to 44.63,
44.66 to 44.70
Multivariate functions, 41.1 to 41.66
Natural logarithms:
antiderivatives (indefinite
integrals) and, 23.10 to
23.22, 23.53, 23.68, 23.69,
23.79,23.80,28.7,28.16,
28.19,28.22, 28.24, 28.55 to
28.57
approximations for, 38.52, 38.53,
39.28, 39.40
defined, 23.1
definite integrals and, 23.36 to
23.38, 23.56, 23.57, 23.59,
23.61,23.63,23.73, 28.25 to
28.31, 32.4, 32.5, 32.8,
32.10, 32.15,32.16, 32.36,
32.37, 32.50
derivatives of, 23.1 to 23.9
graphs of, 23.39, 23.40, 23.46,
23.47, 23.55, 23.76, 25.54,
25.55
inequalities for, 23.41, 23.42,
23.60, 23.77
limits and, 22.43 to 22.45, 23.52,
23.71,23.72
Natural logarithms (Con?.):
Maclaurin series and, 39.5,
39.20, 39.28, 39.34, 39.40,
39.46, 39.50
power series and, 38.38, 38.50 to
38.53, 38.60, 38.86, 38.88,
38.94, 38.99,38.100
properties of, 23.27 to 23.34,
23.64,24.1 to 24.6, 24.35,
24.65 to 24.71
Simpson's rule approximations
for, 23.73
Taylor series and, 39.6
trapezoidal rule approximations
for, 23.57
(See also Exponential functions)
Newton's law of cooling, 26.22,
26.39
Newton's second law of motion,
19.95, 19.%
Normal acceleration, 34.106 to
34.108
Normal distribution:
approximations for, 38.46, 39.41
power series for, 38.45
Normal lines, 8.16, 8.19,8.33,
8.36,8.37,9.14,9.19, 10.23,
10.28, 34.27,42.117
Normal planes, 42.120, 42.121,
45.3, 45.4, 45.6
Normal vectors, 42.105 to 42.115,
42.122 to 42.126, 45.19
Odd functions, 5.43, 5.44, 5.46, 5.49,
5.51,5.52, 5.54 to 5.56, 5.90
to 5.92, 8.46, 8.47, 15.34,
15.47, 15.51,20.48,20.49,
24.97, 38.74, 38.93
One-one functions, 5.57, 5.58,
5.60, 5.63, 5.69 to 5.74,
5.92, 5.93, 5.100, 9.49
One-sided limits, 6.5, 6.33 to 6.36,
6.39
Orthogonal trajectories, 46.22 to
46.24
Osculating planes, 45.18 to 45.20
p-series, 37.40, 37.44, 37.47, 37.54,
37.69, 37.74, 37.78, 37.82,
37.85, 37.88, 37.89, 37.95,
38.11, 38.21
Pappus's theorem for volume,
31.33 to 31.35
Parabolas:
as contours (level curves), 41.35,
41.38, 41.42
curvature (K) of, 34.98
graphs of, 5.1,5.2, 5.11,5.101,
8.44, 15.30, 16.2, 16.47,
34.3, 34.4,34.7,35.15,41.19
Parabolas (Cont.):
intersections of lines with, 3.80
intersections of, 12.45
latus rectum of, 44.80
parametric equations of, 34.3,
34.4, 34.7
in polar coordinates, 35.15
tangents to, 8.28
vertex of, 15.30, 21.13,21.15,
21.22,21.23
Paraboloids:
equations for, 41.80
graphs of, 41.4, 41.5, 41.9, 41.17,
41.25
as ruled surfaces, 41.30
Parallel lines, 3.12 to 3.15, 3.23,
3.24, 3.66, 3.68, 8.23, 40.72
to 40.74
Parallel planes, 40.90, 40.91
Parallel vectors, 33.4, 33.5, 33.36,
33.39, 40.68
Parallelepipeds, 40.45, 40.49,
40.56, 40.63
Parallelogram law for vectors,
33.17
Parallelograms:
area of, 40.43, 40.110,40.111
diagonals of, 33.26, 33.30
quadrilaterals and, 3.42
rhombuses as, 3.76
vertices of, 3.28, 40.109
Parametric equations, 34.1 to
34.42, 40.69 to 40.79,
40.85
Partial derivatives, 42.1 to 42.126
Partial differential equations:
Cauchy-Riemann equations,
42.54, 42.92
Laplace's equation, 42.52 to
42.54
wave equation, 42.55 to 42.58
Partial fractions, 30.1 to 30.33,
46.22
Partial sums, 37.4, 37.5, 37.10,
37.17 to 37.22, 37.24,37.25
Perimeter:
circle, 16.46
rectangle, 16.1, 16.15, 16.29,
16.35, 16.41, 16.44, 16.46,
16.60
triangle, 16.19, 16.20, 16.55,
16.60, 16.61
Period of trigonometric functions,
10.12, 10.13, 10.45
Perpendicular bisectors, 3.35,
3.74
Perpendicular lines, 3.20 to 3.23,
3.25, 3.26, 3.31, 3.69, 40.75,
40.77
Perpendicular planes, 40.95