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Precautions for Differential Calculation Only
• If convergence to a solution cannot be found when
tol
value will be adjusted automatically to determine the solution.
• Non-consecutive points, abrupt fluctuation, extremely large or small points,
inflection points, and the inclusion of points that cannot be differentiated,
or a differential point or differential calculation result that approaches zero
can cause poor precision or error.
Tips for Successful Integration Calculations
When a periodic function or integration interval results in positive and
f
x
negative
(
) function values
Perform separate integrations for each cycle, or for the positive part and the
negative part, and then combine the results.
S
S
Positive
Positive
When integration values fluctuate widely due to minute shifts in the
integration interval
Divide the integration interval into multiple parts (in a way that breaks areas
of wide fluctuation into small parts), perform integration on each part, and
then combine the results.
f (x)
f (x)
a
a
x
x
x
x
0
0
1
1
2
2
Examples
1 1
sin 30°= 0.5
0.5 = 30° bv 1s(sin
−1
sin
sinh 1 = 1.175201194
2 2
–1
cosh
1 = 0
π /2 radians = 90°, 50 grads = 45°
3 3
(15(π)/ 2 )1G(DRG')c(
To calculate
4 4
1N(SETUP)7(Sci)3
B
b
log
1000 = log 1000 = 3
5 5
10
log
16 = 4
2
S
S
Negative
Negative
x
x
x
x
b
b
3
3
4
4
bv
50 1G(DRG')d(
× 2 to three significant digits (Sci 3)
e
5
B
b
b
∫
∫
f(x)dx =
f(x)dx =
a
a
Positive Part
Positive Part
S
S
(
(
b
b
∫
∫
f(x)dx =
f(x)dx =
a
a
b
b
∫
∫
+
+
f(x)dx
f(x)dx
x
x
x
x
4
4
s 30 )=
−1
) 0.5 )=
wb(sinh) 1 )=
wf(cosh
−1
v
1i(%) 5 e* 2 =
1i(%) 5 )* 2 =
l 1000 )=
l 2 1)(,) 16 )=
& 2 e 16 =
EN-18
tol
input is omitted, the
c
c
b
b
∫
∫
∫
∫
f(x)dx +
f(x)dx +
f(x)dx
f(x)dx
a
a
c
c
Negative Part
Negative Part
S
S
Positive)
Positive)
(
(
Negative)
Negative)
x
x
x
x
∫
∫
∫
∫
1
1
2
2
f(x)dx +
f(x)dx +
f(x)dx + .....
f(x)dx + .....
x
x
a
a
1
1
1.175201194
) 1 )=
r
)=
g
)=
0.5
30
0
90
45
2
2.97×10
2
2.97×10
3
4
4
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