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托马斯微积分英文原版第15版;全彩;pdf带书签
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托马斯微积分英文原版 第15版 Thomas’ Calculus꞉ Early Transcendentals, 15th Edition
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About the artist: Thomas Lin Pedersen is a generative artist in Denmark who mainly works on capturing dynamic systems
as still imagery. Thomas’s work is mainly programmed in R and the results are presented as they come out of the
algorithm with no post-production applied. See more at https://data-imaginist.com/art
About the cover: The Folding Flow Series is based on a 3-D ow eld created using Simplex noise. The surface is segmented
into distinct areas that have dierent depth proles but share x and y values. Each line in the resulting piece is made by
selecting a random point and tracing its path in the ow eld according to the depth prole of the area it started in. The
end result is range of lines that all share the same 2-dimensional ow but have areas that divert and fold into each other.
Arithmetic Operations
()
+= +⋅=ab cabac
a
b
c
d
ac
bd
,
+=
+
=⋅
a
b
c
d
ad bc
bd
ab
cd
a
b
d
c
,
Laws of Signs
()
−−
=
−
=− =
−
aa
a
b
a
b
a
b
,
Zero Division by zero is not defined.
≠=
==
a
a
aIf 0:
0
0, 1,
00
a0
⋅=⋅=aa aFor any number: 00 0
Laws of Exponents
()
()
=====
+
aa
aababaaa
aa
,,() ,
mn mn
m
mm mn mn
mn
m
n
n
m
If
≠a 0,
then
===
−−
a
a
aa a
a
,1,
1
.
m
n
mn m
m
0
The Binomial Theorem For any positive integer n,
(
)
()
+=++
−
⋅
−−
ab anab
nn
ab
1
12
n
nn n
122
()()
+
−−
⋅⋅
++ +
−−
nn n
ab nab b
12
123
.
nn
n33 1
For instance,
() ()
() ()
+=++ −=−+
+=+++−=−
+−
ab aabb ab aabb
ab aababb ab aaba
bb
2, 2
33
,33.
2
22
2
22
3
32 23
3
32
23
Factoring the Dierence of Like Integer Powers,
>n 1
()
()
−=−+++++
−− −−−
a baba abab ab b
nn nn nnn12 32 21
For instance,
()
()
()()
()
()
−=−+
−=−++
−=−+
++
ab
abab
ab
abaabb
ab
abaaba
bb
,
,
.
22
33
22
44 32
23
Completing the Square If
≠a 0,
then
()
()
++=+ =+ =−
ax
bx cauC ux ba Cc
b
a
2,
4
.
22
2
The Quadratic Formula
If
≠a 0
and
++=axbxc 0,
2
then
=
−± −
x
bb ac
a
4
2
.
2
Basic Algebra Formulas
Parallelogram
h
b
A = bh
Trapezoid
h
a
b
A = (a + b)h
1
2
Circle
r
A = pr
2
,
C = 2pr
=A area,
=B areaofbase,
=C circumference,
=S surfacearea,
=V volume
Triangle
b
h
A = bh
1
2
Similar Triangles
b
b′
c′ a′
ac
a′
a
=
b′
b
=
c′
c
Pythagorean Theorem
c
b
a
a
2
+ b
2
= c
2
Geometry Formulas
Any Cylinder or Prism with Parallel Bases
h
B
h
B
V = Bh
Right Circular Cylinder
h
r
V = pr
2
h
S
= 2prh =
Area of side
Any Cone or Pyramid
V = Bh
3
1
h
B
h
B
Right Circular Cone
V = pr
2
h
1
3
S = prs =
Area of side
Sphere
V = pr
3
, S = 4pr
2
4
3
Based on the original work by
GEORGE B. THOMAS, JR.
Massachusetts Institute of Technology
as revised by
JOEL HASS
University of California, Davis
CHRISTOPHER HEIL
Georgia Institute of Technology
PRZEMYSLAW BOGACKI
Old Dominion University
MAURICE D. WEIR
Naval Postgraduate School
FIFTEENTH EDITION
Early Transcendentals
CALCULUS
THOMAS’
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