# HP F2226A - 48GII Graphic Calculator User Manual Page 492

Graphing calculator.

Now, use '(-X)^3*EXP(-a*X)' ` LAP µ. The result is exactly the same.
Integration theorem. Let F(s) = L{f(t)}, then
L
Convolution theorem. Let F(s) = L{f(t)} and G(s) = L{g(t)}, then
t
L
f
0
L
Example 4 – Using the convolution theorem, find the Laplace transform of
(f*g)(t), if f(t) = sin(t), and g(t) = exp(t). To find F(s) = L{f(t)}, and G(s) = L{g(t)},
use: 'SIN(X)' ` LAP µ. Result, '1/(X^2+1)', i.e., F(s) = 1/(s
Also, 'EXP(X)' ` LAP. Result, '1/(X-1)', i.e., G(s) = 1/(s-1). Thus, L{(f*g)(t)}
2
= F(s)⋅G(s) = 1/(s
+1)⋅1/(s-1) = 1/((s-1)(s
Shift theorem for a shift to the right. Let F(s) = L{f(t)}, then
Shift theorem for a shift to the left. Let F(s) = L{f(t)}, and a >0, then
L
{
(
f
Similarity theorem. Let F(s) = L{f(t)}, and a>0, then
(1/a)⋅F(s/a).
Damping theorem. Let F(s) = L{f(t)}, then L{e
Division theorem. Let F(s) = L{f(t)}, then
1
t
(
)
(
).
f
u
du
F
s
0
s
(
)
(
)
=
L
{(
u
g
t
u
du
f
{
f
(
t
)}
L
{
g
(
t
)}
F
(
s
2
+1)) = 1/(s
–as
⋅L{f(t)} = e
L{f(t-a)}=e
as
)}
(
)
t
a
e
F
s
–bt
*
)(
)}
=
g
t
)
G
(
s
)
2
+1).
3
2
-s
+s-1).
–as
⋅F(s).
a
st
) (
.
f
t
e
dt
0
L{f(a⋅t)} =
⋅f(t)} = F(s+b).
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