Numerical mathematic and computing.pdf

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Numerical Mathematics and Computing
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Formulas from Algebra
1
+
r
+
r 2
+···+
r n − 1
=
r n
−
1
log a x
= (
log a b
)(
log b x
)
r
−
1
1
+
2
+
3
+···+
n
=
2 n
(
n
+
1
)
|
x
|−|
y
| |
x
±
y
| |
x
|+|
y
|
1 2
+
2 2
+
3 2
+···+
n 2
=
6 n
(
n
+
1
)(
2 n
+
1
)
Cauchy-Schwarz Inequality
n
2
n
n
x i y i
x i
y i
i
=
1
=
1
i
=
1
Formulas from Geometry
Area of circle: A
= π
r 2
( r
=
radius)
Circumference of circle: C
=
2
π
r
Area of trapezoid: A
=
2 h
(
a
+
b
)
( h
=
height; a and b are parallel bases)
Area of triangle: A
=
2 bh
( b
=
base, h
=
height)
Formulas from Trigonometry
sin 2 x
+
cos 2 x
=
1
sin 2
−
x =
cos x
cos 2
x =
1
+
tan 2 x
=
sec 2 x
−
sin x
sin x
=
1
/
csc x
sin
(
x
+
y
) =
sin x cos y
+
cos x sin y
cos x
=
1
/
sec x
cos
(
x
+
y
) =
cos x cos y
−
sin x sin y
2 sin 2 (
) cos 2 (
)
tan x
=
1
/
cot x
sin x
+
sin y
=
x
+
y
x
−
y
2 cos 2 (
) cos 2 (
)
tan x
=
sin x
/
cos x
cos x
+
cos y
=
x
+
y
x
−
y
sin x
=−
sin
( −
x
)
sinh x
=
2 (
e x
−
e − x
)
cos x
=
cos
( −
x
)
cosh x
=
2 (
e x
+
e − x
)
Graphs
y
tan x
y
arccos x
1
sin x
cos x
arcsin x
2
arctan x
x
2
3 – 2
2
1
x
1
0
1
2
1
1
i
1
1
1
1
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Formulas from Analytic Geometry
Slope of line: m
=
y 2 −
y 1
(two points
(
x 1 ,
y 1 )
and
(
x 2 ,
y 2 )
)
x 2 −
x 1
Equation of line: y
−
y 1 =
m
(
x
−
x 1 )
Distance formula: d
=
(
x 2 −
x 1 )
2
+ (
y 2 −
y 1 )
2
Circle:
(
x
−
x 0 )
2
+ (
y
−
y 0 )
2
=
r 2
( r
=
radius,
(
x 0 ,
y 0 )
center)
Ellipse: (
x
−
x 0 )
2
+ (
y
−
y 0 )
2
=
1( a and b semiaxes)
a 2
b 2
Definitions from Calculus
The limit statement lim
x → a
f
(
x
) =
L means that for any
ε>
0, there is a
δ>
0 such that
|
f
(
x
) −
L
| <ε
.
A function f is continuous at x if lim
h → 0
< |
x
−
a
| <δ
f
(
x
+
h
) =
f
(
x
)
.
If lim
h →
1
h [ f
(
x
+
h
) −
f
(
x
)
] exists, it is denoted by f (
x
)
or
d
dx
f
(
x
)
and is termed the derivative of f at x .
0
Formulas from Differential Calculus
(
f
±
g
) =
f ±
g
d
dx log a x
=
x − 1 log a e
d
dx arccot x
=
−
1
1
+
x 2
(
fg
) =
fg
+
f g
d
dx sin x
=
cos x
d
dx arcsec x
=
1
x √ x 2
−
1
f
g
=
gf −
fg
d
dx cos x
=−
sin x
d
dx arccsc x
=
1
x √ x 2
−
−
1
g 2
(
f
◦
g
) = (
f ◦
g
)
g
d
dx tan x
=
sec 2 x
d
dx sinh x
=
cosh x
d
dx x a
=
ax a − 1
d
dx cot x
=−
csc 2 x
d
dx cosh x
=
sinh x
d
dx e x
=
e x
d
dx sec x
=
tan x sec x
d
dx tanh x
=
sech 2 x
d
dx e ax
=
ae ax
d
dx csc x
=−
cot x csc x
d
dx coth x
=−
csch 2 x
d
dx a x
=
a x
ln a
d
dx arcsin x
=
√ 1
1
d
dx sech x
=−
sech x tanh x
−
x 2
d
dx x x
=
x x
(
1
−
ln x
)
d
dx arccos x
=
√ 1
−
1
d
dx csch x
=−
csch x coth x
−
x 2
d
dx ln x
=
x − 1
d
dx arctan x
=
1
1
+
x 2
whenever 0
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SIXTH EDITION
MATHEMATICS
AND COMPUTING
AND COMPUTING
Ward Cheney
The University of Texas at Austin
David Kincaid
The University of Texas at Austin
Australia
•
Brazil
•
Canada
•
Mexico
•
Singapore
•
Spain
nited Kingdom
•
nited States
NUMERICAL
NUMERICAL
MATHEMATICS
395025518.002.png 395025518.003.png
Numerical Mathematics and Computing, Sixth edition
Ward Cheney, David Kincaid
Dedicated to David M. Young
Publisher: Bob Pirtle
Development Editor: Stacy Green
Editorial Assistant: Elizabeth Rodio
Technology Project Manager: Sam Subity
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Creative Director: Rob Hugel
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Print Buyer: Doreen Suruki
Permissions Editor: Bob Kauser
Production Service: Matrix Productions
Text Designer: Roy Neuhaus
Photo Researcher: Terri Wright
Copy Editor: Barbara Willette
Illustrator: ICC Macmillan Inc.
Cover Designer: Denise Davidson
Cover Image: Glowimages/Getty Images
Cover Printer: R.R. Donnelley/Crawfordsville
Compositor: ICC Macmillan Inc.
Printer: R.R. Donnelley/Crawfordsville
© 2008, 2004 Thomson Brooks/Cole, a part of The Thomson
Corporation. Thomson, the Star logo, and Brooks/Cole are
trademarks used herein under license.
ALL RIGHTS RESERVED. No part of this work covered by the
copyright hereon may be reproduced or used in any form or by
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Printed in the United States of America
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Student Edition:
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