Quadratic Differential Calculations - Casio Algebra FX 2.0 PLUS User Manual

k k k k k Quadratic Differential Calculations
After displaying the function analysis menu, you can input quadratic differentials using either of
the two following formats.
K4(CALC)c(
––– (f (x), a) ⇒ ––– f (a)
dx
Quadratic differential calculations produce an approximate differential value using the following
second order differential formula, which is based on Newton's polynomial interpretation.
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) –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
=
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
Here we will use a tolerance tol = 1
Input the function f(
AK4(CALC)c(
evx+v-g,
Input 3 as point
d,
Input the tolerance value.
bE-f)
w
# In the function f(x), only X can be used as a
variable in expressions. Other variables (A
through Z, r, θ ) are treated as constants, and
the value currently assigned to that variable is
applied during the calculation.
Numerical Calculations
d 2 dx
/
a
differential coefficient point , tol: tolerance)
( :
d 2 d 2
2 2
dx
y
= 3 for the function
x
).
d
a
, which is the differential coefficient point.
2-5-5
2 f(x) a
)
, ,tol)
180h
2
x x x
+ 4 – 6
= +
3 2
– 5
E
dx
/ ) vMd+
2 2
# Input of the tolerance (tol) value and the closing
parenthesis can be omitted.
# Discontinuous points or sections with drastic
fluctuation can adversely affect precision or
even cause an error.
20010101 20011101
[OPTN]-[CALC]-[d /dx
2
]
2