58
3-3 Quadratic Differential Calculations
After displaying the function analysis menu, you can input quadratic differentials
using either of the two following formats.
3
(
d
2
/
dx
2
)
f(x)
,
a
,
n
)
Quadratic differential calculations produce an approximate differential value using
the following second order differential formula, which is based on Newton's
polynomial interpretation.
–
f(x – 2h) + 16 f (x – h) – 30 f(x) + 16 f(x + h) – f(x + 2h)
f''(x)
=
–––––––––––––––––––––––––––––––––––––––––––––––
12h
2
In this expression, values for “sufficiently small increments of
x
” are sequentially
calculated using the following formula, with the value of
m
being substituted as
m
= 1, 2, 3 and so on.
1
h = ––––
5
m
The calculation is finished when the value of
f " (x)
based on the value of
h
calculated using the last value of
m
, and the value of
f "(x)
based on the value of
h
calculated using the current value of
m
are identical before the upper
n
digit is
reached.
• Normally, you should not input a value for
n
. It is recommended that you only
input a value for
n
when required for calculation precision.
• Inputting a larger value for
n
does not necessarily produce greater precision.
u
u
u
u
u
To perform a quadratic differential calculation
Example
To determine the quadratic differential coefficient at the point
where
x
= 3 for the function
y
=
x
3
+
4
x
2
+
x
– 6
Here we will use a final boundary value of
n
= 6.
Input the function
f(
x
)
.
A
K
4
(CALC)
3
(
d
2
/
dx
2
)
v
M
d+
e
vx
+
v
-g,
[OPTN]
-
[CALC]
-
[
d
2
/
dx
2
]
d
2
d
2
–––
( f (x), a, n)
%
–––
f (a)
dx
2
dx
2
Final boundary (
n
= 1 to 15)
Differential coefficient point
Summary of Contents for CFX-9970G
Page 22: ... CFX 9970G ...
Page 452: ...435 1 2 3 4 5 Program for Circle and Tangents No 4 Step Key Operation Display ...
Page 453: ...436 Program for Circle and Tangents No 4 Step Key Operation Display 6 7 8 9 10 ...
Page 454: ...437 11 12 13 14 15 Program for Circle and Tangents No 4 Step Key Operation Display ...
Page 455: ...438 16 17 18 Program for Circle and Tangents No 4 Step Key Operation Display ...
Page 458: ...441 1 2 3 4 5 Program for Rotating a Figure No 5 Step Key Operation Display ...
