# Laplace Transform Theorems - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

function LAP you get back a function of X, which is the Laplace transform of
f(X).
Example 2 – Determine the Laplace transform of f(t) = e
'EXP(2*X)*SIN(X)' ` LAP The calculator returns the result: 1/(SQ(X-2)+1).
Press µ to obtain, 1/(X
When you translate this result in paper you would write
F
(
Example 3 – Determine the inverse Laplace transform of F(s) = sin(s). Use:
'SIN(X)' ` ILAP.
The calculator takes a few seconds to return the result:
'ILAP(SIN(X))', meaning that there is no closed-form expression f(t), such that f(t)
-1
= L
{sin(s)}.
Example 4 – Determine the inverse Laplace transform of F(s) = 1/s
'1/X^3' ` ILAP µ. The calculator returns the result: 'X^2/2', which is
-1
3
interpreted as L
{1/s
} = t
Example 5 – Determine the Laplace transform of the function f(t) = cos (a⋅t+b).
Use: 'COS(a*X+b)' ` LAP . The calculator returns the result:
Press µ to obtain –(a sin(b) – X cos(b))/(X
interpreted as follows: L {cos(a⋅t+b)} = (s⋅cos b – a⋅sin b)/(s

## Laplace transform theorems

To help you determine the Laplace transform of functions you can use a
number of theorems, some of which are listed below. A few examples of the
theorem applications are also included.
Differentiation theorem for the first derivative. Let f
for f(t), i.e., f(0) = f
o
2
-4X+5).
2
t
s
)
L
{
e
sin
t
}
2
s
2
/2.
, then
2t
⋅sin(t). Use:
1
4
s
5
3
. Use:
2
2
+a
).
The transform is
2
2
+a
).
be the initial condition
o
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