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circuits. In most cases one is interested in the system response after time t>0,
thus, the definition of the Laplace transform, given above, involves an
integration for values of t larger than zero.
The inverse Laplace transform maps the function F(s) onto the original function
f(t) in the time domain, i.e., L
-1
{F(s)} = f(t).
The convolution integral or convolution product of two functions f(t) and g(t),
where g is shifted in time, is defined as
Laplace transform and inverses in the calculator
The calculator provides the functions LAP and ILAP to calculate the Laplace
transform and the inverse Laplace transform, respectively, of a function f(VX),
where VX is the CAS default independent variable, which you should set to ‘X’.
Thus, the calculator returns the transform or inverse transform as a function of
X. The functions LAP and ILAP are available under the CALC/DIFF menu. The
examples are worked out in the RPN mode, but translating them to ALG mode
is straightforward. For these examples, set the CAS mode to Real and Exact.
Example 1 – You can get the definition of the Laplace transform use the
following: ‘
f(X)
’
`
LAP
in RPN mode, or
LAP(f(X))
in ALG mode.
The calculator returns the result (RPN, left; ALG, right):
Compare these expressions with the one given earlier in the definition of the
Laplace transform, i.e.,
∫
∞
−
⋅
=
=
0
,
)
(
)
(
)}
(
{
dt
e
t
f
s
F
t
f
st
L
and you will notice that the CAS default variable X in the equation writer
screen replaces the variable s in this definition. Therefore, when using the
.
)
(
)
(
)
)(
*
(
0
∫
⋅
−
⋅
=
t
du
u
t
g
u
f
t
g
f
