Chapter 2: Main Application
52
Condition Judgment (judge, piecewise)
u
“judge” Function
The “judge” function returns TRUE when an expression is true, and FALSE when it is false.
Problem
Operation
Is the following expression true or false?
1 = 1
TRUE
[judge]
1
=
1
w
Is the following expression true or false?
1 < 0
FALSE
[judge]
1
<
0
w
u
“piecewise” Function
The “piecewise” function returns one value when an expression is true, and another value when the expression
is false.
The syntax of the “piecewise” function is shown below.
piecewise(<condition expression>, <return value when true>, <return value when false or indeterminate> [ ) ]
or
piecewise(<condition expression>, <return value when true>, <return value when false>, <return value when
indeterminate> [ ) ]
Use the soft keyboard (
1
) to input “piecewise” function according to the syntax shown below.
or
<return value when true>, <condition expression>
<return value when false or indeterminate>
<return value when condition 1 is true>, <condition 1 expression>
<return value when condition 2 is true>, <condition 2 expression>
Problem
Operation
For the expression 0
t
x
(
x
= variable), return 1
when
x
is 0 or less, and 2 when
x
is greater than 0
or undefined.
[piecewise]
0
:
X
,
1
,
2
w
or
1
1
c
2
ef
0
:
X
w
For the expression 1
t
x
(
x
= variable), return 1
when
x
is 1 or less, and 2 when
x
is greater than 1.
1
1
c
2
ef
1
:
X
c
1
<
X
w
Angle Symbol (
∠
)
Use this symbol to specify the coordinate format required by an angle in a vector.
You can use this symbol for a vector only.
Problem
Operation
Convert the polar coordinates
r
=
'
2 ,
θ
=
π
/4 to
rectangular coordinates.
[1, 1]
Change the [Angle] setting to “Radian”.
[toRect]
[
5
2
e
,
~
7
/
4
)]
w
Derivative Symbol (’)
A single derivative symbol indicates the first derivative of an equation in the format: <variable name>’.
Problem
Operation
Solve the differential equation
y
’ =
x
.
{
y
= 0.5 ·
x
2
+ const (1)}
+Y
'
=
X
,
X
,
Y
w
Important!
The “dSolve” function can solve differential equations up to three degrees, so a maximum of three derivative
symbols (
y
’’’) can be used. Executing a “dSolve” calculation that has more than three derivative symbols will
result in an Invalid Syntax error.
