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20061001
k Quadratic Differential Calculations [OPTN]-[CALC]-[d
2
/dx
2
]
After displaying the function analysis menu, you can input quadratic differentials using the
following syntax.
K4(CALC)3(d
2
/dx
2
) f(x),a,tol)
(a: differential coefficient point, tol: tolerance)
Quadratic differential calculations produce an approximate differential value using the
following second order differential formula, which is based on Newton’s polynomial
interpretation.
In this expression, values for “sufficiently small increments of h” are used to obtain a value
that approximates f ”(a).
Example To determine the quadratic differential coefficient at the point where
x = 3 for the function y = x
3
+ 4x
2
+ x – 6
Here we will use a tolerance tol = 1E – 5
Input the function f(x).
AK4(CALC)3(d
2
/dx
2
) vMd+
evx+v-g,
Input 3 as point a, which is the differential coefficient point.
d,
Input the tolerance value.
bE-f)
w
d
2
d
2
––– (
f
(
x
),
a
)
⇒
–––
f
(
a
)
dx
2
dx
2
d
2
d
2
––– (
f
(
x
),
a
)
⇒
–––
f
(
a
)
dx
2
dx
2
f
''(a) =
180h
2
2 f(a + 3h) – 27 f(a + 2h) + 270 f(a + h) – 490 f(a) + 270 f(a – h) – 27 f(a –2h) + 2 f(a – 3h)
f
''(a) =
180h
2
2 f(a + 3h) – 27 f(a + 2h) + 270 f(a + h) – 490 f(a) + 270 f(a – h) – 27 f(a –2h) + 2 f(a – 3h)
2-5-5
Numerical Calculations
# In the function f(x), only X can be used as
a variable in expressions. Other variables
(A through Z excluding X, r, θ) are treated
as constants, and the value currently
assigned to that variable is applied during the
calculation.
# Input of the tolerance (
tol) value and the closing
parenthesis can be omitted.
# Specify a tolerance (tol) value of 1E-14 or
greater. An error (Time Out) occurs whenever
no solution that satisfies the tolerance value can
be obtained.
20070101