REFERENCE PAGES
Algebra
Geometry
Arithmetic Operations
Geometric Formulas
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Formulas for area A, circumference C, and volume V:
Triangle
A 1 bh
2
1 ab sin
2
a
Expo
5E-18(pp 1176-1185)
1/19/06
3:42 PM
Page 1176
CHAPTER 18
The charge in an electric
circuit is governed by the
differential equations that
we solve in Section 18.3.
Second-Order Differential Equations
5E-18(pp 1176-1185)
1/19/06
3:42 PM
Page 1177
The basi
5E-16(pp 1016-1025)
1/18/06
4:13 PM
Page 1016
CHAPTER 16
If we approximate a solid by rectangular columns
and let the number of columns increase, the
limit of sums of volumes of columns is the volume
of the solid.
Multiple Integrals
5E-16(pp 1016-1025)
1
5E-14(pp 884-893)
1/18/06
11:47 AM
Page 884
CHAPTER 14
The calculus of vectorvalued functions is used
in Section 14.4 to prove
Kepler’s laws. These
describe the motion of
the planets about the Sun
and also apply to the orbit
of a satellite about the
Earth
5E-13(pp 828-837)
1/18/06
11:09 AM
Page 828
CHAPTER 13
Wind velocity is a vector because
it has both magnitude and direction. Pictured are velocity vectors
indicating the wind pattern over
San Francisco Bay at 12:00 P.M.
on June 11, 2002.
Vectors and the
5E-12(pp 736-745)
1/18/06
10:08 AM
Page 736
CHAPTER 12
Bessel functions, which are
used to model the vibrations of drumheads and
cymbals, are deﬁned as
sums of inﬁnite series in
Section 12.8. Notice how
closely the computergenerated models (which
involve
5E-11(pp 686-695)
1/18/06
9:31 AM
Page 686
CHAPTER 11
Parametric curves are used to
represent letters and other symbols on laser printers. See the
Laboratory Project on page 705.
Parametric Equations and
Polar Coordinates
5E-11(pp 686-695)
1/18/06
9:31 A
5E-10(pp 622-631)
1/18/06
9:18 AM
Page 622
CHAPTER 10
By analyzing pairs of differential equations we gain
insight into population
cycles of predators and
prey, such as the Canada
lynx and snowshoe hare.
W
150
100
R
3000
W
R
W
50
120
2000
80
0
1000
2000
3
5E-09(pp 582-591)
1/17/06
6:20 PM
Page 582
CHAPTER 9
Integration enables us to
calculate the force exerted
by water on a dam.
Further Applications of Integration
5E-09(pp 582-591)
1/17/06
6:20 PM
Page 583
We looked at some applications of integrals in Ch
5E-08(pp 510-519)
1/17/06
5:19 PM
Page 510
CHAPTER 8
The techniques of this
chapter enable us to ﬁnd
the height of a rocket a
minute after liftoff and to
compute the escape
velocity of the rocket.
Techniques of Integration
5E-08(pp 510-519)
1/17/06
5:19
5E-05(pp 314-323)
1/17/06
3:37 PM
Page 314
CHAPTER 5
To compute an area we approximate a region by rectangles
and let the number of rectangles become large. The precise
area is the limit of these sums of areas of rectangles.
Integrals
5E-05(pp 314-323)
1
5E-04(pp 222-231)
1/17/06
2:40 PM
Page 222
CHAPTER 4
Scientists have tried to
explain how rainbows are
formed since the time of
Aristotle. In the project on
page 232, you will be able
to use the principles of
differential calculus to
explain the formation
5E-03(pp 126-135)
1/17/06
1:49 PM
Page 126
CHAPTER 3
By measuring slopes at points on the sine curve,
we get strong visual evidence that the derivative
of the sine function is the cosine function.
Derivatives
5E-03(pp 126-135)
1/17/06
1:49 PM
Page 127
In
5E-02(pp 064-073)
1/17/06
1:24 PM
Page 64
CHAPTER 2
The idea of a limit is
illustrated by secant lines
approaching a tangent line.
Limits and Rates of Change
5E-02(pp 064-073)
1/17/06
1:25 PM
Page 65
In A Preview of Calculus (page 2) we saw how the idea
5E-FM.qk
1/19/06
11:09 AM
Page 1
CA L C U L U S
5E-Preview (pp 02-09)
1/17/06
11:44 AM
Page 2
By the time you ﬁnish this course, you will
be able to explain the formation and location
of rainbows, compute the force exerted by
water on a dam, analyze the