Casio FX-795P User Manual

72
4-4
Numeric
Solution
of
Equations
Numeric
solution
of
an
equation
is
a
method
of
assigning
an
initial
solution
x
(approximate)
and
obtaining
a
more
accurate
approximate
solution
x.
(See
diagram below.)
With
the
initial
solution
as
x5,
obtain
tangent
line:
7,
in
(%o,
f(Xo)),
and
with
x,
as
the
intersection
of
axis
J;
and
x,
and
in
the
same
manner
obtain
tangent
I,
in
(¢1,
f(%2)),
and
continue
in
this
manner
to
Xn
(n
times).
Ending
condition
is
the
solution
to
xn
when
\xn
-
xn-1
|<
relative
error.
Also,
if
the
value
is
greater
than
the
number
of
loops
set
by
n,
the
equation
will
not
be
solved
(when
diverged
or
when
the
yalue
near
the
solution
changes
greatly.)
This
method
is
called
the
Newton’s
method.
This
method
can
be
used
in
this
unit
for
numeric
solution
of
equations.
The
primary
derivative
(function
derived
from
one
differentiation
of
f(x))
is
obtained
to
obtain
the
tangent,
and
the
minimal
interval
h
is
set
and
the
straight
line
passing
through
the
two
points
(xk,
f(ck)),
(xk
+
h
(A)),
{@k
+
h
(A))
is
con-
sidered
the
tangent
in
this
computer.
y= f(x)
&xtl1
h(o)
ax .arth(s)
©
Numeric
Solution
of
Equations
Menu
To
obtain
the
numeric
solution
of'an
equation,
start
by
selecting
Newt
(press
the
(%)
key)
from
the
software
menu.
The
numeric
solution
of
the
equation
menu
will
be
displayed
as
follows.
BUZZER RUN DEG
4-4 Numeric Solution of Equations
The
following
processes
can
be
selected
from
this
menu,
H.....
(F(X)
Input
and
calculation
of
function
and
initial
value
G..... (0.4) Confirmation of result
®).....
(H(A))
Setting
of
the
minimal
interval
when
calculating
the
derivative
:
,
@.....
(Err)
Input
of
relative
error
range
(Err)
and
maximum
number
of
loops
(Maxloop)
,
The functions that can be used are as follows.
+,7,%,
7,
1,
SIN,
COS,
TAN,
ASN,
ACS,
ATN,
LOG,
LN,
EXP,
SQR,
HYP
The
variable
of
the
function
f(x)
must
be
recorded
as
X.
Set
the
input
range
of
Err
as
greater
than
1E98.
Excessively
small
values
are
meaningless
since
internal
calculation.
is
performed
with
12
digits.
Example: *
Obtain
the
solution
of
f(x)
=
0.
when
f(x)
=
2x3
+
3x?
-
x
-
5
with
the
relative
error
0.0001
and
maximum
number
of
loops
of
30.
f(x) =223 4322-45
yy =f(2)
73

Casio FX-795P Specifications

General

Brand	Casio
Model	FX-795P
Category	Desktop
Language	English