Casio CFX-9800G - Page 58

Chapter 3 Hil Differential, Integration, and & Calculations
3-1 How the Unit Calculates Differentials
The following is the input format for differentials:
SEBS)
a JAxD.
T__ increase/decrease of x
Point for which you want to determine the derivative
d/dx(f(x), a, Ax) > £ Ha)
The differentiation for this type of calculation is defined as:
S(at+ Ax)—-f(a)
S’(aj=lim ie
Ax>0
In this definition, infinitesimal is replaced by a sufficiently small Ax, with the value in the
neighborhood of /” (a) calculated as:
»(q) - f+ 4- Fla)
£03
In order to provide the best precision possible, this unit employs central difference to per-
form differential calculations. The following illustrates central difference.
y
+
oy v=S()
Slat Ax)—fla— Ax)
vy
Vx
Xx
0 a-Ax a a+Ax
The
slopes
of
point
a
and
point
2+
Ax,
and
of
point
@
and
point
a—
Ax
in
function
y=
f(x)
are
as
follows:
Sa+Ax)—
fla)
_
dy,
fla) fla—
Ax)
_
VW
Ax
Ax
Ax
vx
—80-—
In the above, Ay/A~x is called the forward difference, while. Vy/ Vx is the backward difference.
To calculate derivatives, the unit takes the average between the value of. Aylax. and Vyl Vx,
thereby providing higher precision for derivatives.
This average, which is called the central difference, is expressed as:
Slat Ax)-fla@) , fa)—fla— 4x)
car ar oe)
_ f(at+ Ax)—fla— Ax)
. 2Ax
MTo Perform a Differential Calculation
Example} To determine the derivative at point x=3 for the function y= xo Ax? +
x—6, when the increase/decrease of x is defined as‘Ax=1e—5.
ale ais #8
Input the function f(x).
[ac] Stas || CRA] PAN eR] ++ (RC) | Eo
|— Jala)
Input point x=< for which you want Fz TE, race aa
to determine the derivative. 23> bg ag
E32) :
Input Ax, which is the increase/ : 7x + +R
decrease of x.
OBO
232 1e-5)_
*X is the only expression that can be used in the function f(x). If you use any other varia-
ble name (A through Z, r, or 4), that variable name is regarded as a constant, using the
current contents of the corresponding value memory in the calculation.
*lnput of Ax for the increase/decreasé of x can be skipped. When you do, the unit auto-
matically uses a value for Ax that is appropriate for the value of x=a, which you speci-
fied as the point for which you wanted to determine the derivative.
«in general, calculation precision is +1 at the feast significant digit of the result.
—8I-