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5/21/2008
http://numericalmethods.eng.usf.edu
1
Forward Divided Difference
Topic: Differentiation
Major: General Engineering
Authors: Autar Kaw, Sri Harsha Garapati
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2
Definition
i
x
.
()
(
)(
)
x
x
f
x
x
f
x
x
f
Δ
Δ
0
Δ
lim
−
+
→
=
′
f(x)
Slope at
x
y
i
x
http://numericalmethods.eng.usf.edu
3
Forward Divided Difference
x
x
Δ
+
x
x
()
( )
x
x
f
x
x
f
x
f
Δ
−
Δ
+
≅
′
( )
x
x
f
x
x
f
x
f
i
i
i
Δ
−
Δ
+
≅
′
)
(
x
f
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4
Example
Example
:
The velocity of a rocket is given by
()
30
0
,
8
.
9
2100
10
14
10
14
ln
2000
4
4
≤
≤
−
⎥
⎦
⎤
⎢
⎣
⎡
−
×
×
=
t
t
t
t
ν
where
given in m/s and
t
is given in seconds
.
Use forward difference approximation of
the first derivative of
( )
t
ν
to calculate the acceleration at
.
16
s
t
=
Use a step size of
.
2
s
t
=
Δ
( )
t
t
ν
t
ν
t
a
i
i
i
Δ
1
−
≅
+
Solution:
16
=
i
t
http://numericalmethods.eng.usf.edu
5
2
Δ
=
t
t
t
t
i
i
Δ
1
+
=
+
18
2
16
=
+
=
()
2
16
18
16
ν
−
=
a
18
8
.
9
18
2100
10
14
10
14
ln
2000
18
4
4
−
⎥
⎦
⎤
⎢
⎣
⎡
−
×
×
=
s
m
/
02
.
453
=
16
8
.
9
16
2100
10
14
10
14
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida  Tampa.
 Spring '08
 Kaw,A

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