STAT 427
Prof. P. Goel
Calculus Review
Note: Good understanding of calculus is essential for your success in Stat 427. Please review the
following concepts by the begining of third week.
•
Function, limit, continuity, differentiation;
•
Infinite sequences and series, Taylor series expansion;
•
Integral of a function on an interval (a, b) equals the area under the curve in (a, b);
•
Techniques of integration  integration by parts, integration by substitution or change of
variables;
•
Multiple integration (functions of two variables).
1
Basic Differentiation Rules
•
dx
n
dx
=
nx
n

1
•
de
x
dx
=
e
x
•
de
u
dx
=
e
u
du
dx
(Chain Rule)
•
da
u
dx
=
a
u
‘n
(
a
)
du
dx
(Chain Rule)
•
d‘n
(
x
)
dx
=
1
x
•
d
(
cf
(
x
))
dx
=
c
df
(
x
)
dx
•
d
(
f
(
x
) +
g
(
x
))
dx
=
df
(
x
)
dx
+
dg
(
x
)
dx
•
d
(
f
(
x
)
g
(
x
))
dx
=
f
(
x
)
dg
(
x
)
dx
+
df
(
x
)
dx
g
(
x
)
•
d
(
f
(
x
)
/g
(
x
))
dx
=
df
(
x
)
dx
g
(
x
)

f
(
x
)
dg
(
x
)
dx
g
(
x
)
2
1
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2
Basic Integration Rules
•
Let
Z
x
a
f
(
u
)
du
=
F
(
x
)
.
Then
F
(
.
)
is called the antiderivative of
f
(
.
)
, and of course,
f
(
.
)
is the derivative of
F
(
.
)
.
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 Spring '08
 Staff
 Calculus, Derivative, Probability, dx, dx dx dx, Calculus Review

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