HP 50g User Manual Page 491

Graphing calculator.

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
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
Similarity theorem. Let F(s) = L{f(t)}, and a>0, then
Damping theorem. Let F(s) = L{f(t)}, then L{e
Division theorem. Let F(s) = L{f(t)}, then
Laplace transform of a periodic function of period T:
Limit theorem for the initial value: Let F(s) = L{f(t)}, then
Limit theorem for the final value: Let F(s) = L{f(t)}, then
t
L
(
)
(
f
u
g
t
0
L
{
f
(
t
)}
L
+1) 1/(s-1) = 1/((s-1)(s
L{f(t-a)}=e
as
{
(
)}
f
t
a
e
) (
f
L
t
{ L
(
)}
f
t
1
f
lim
0
t
0
)
L
{(
u
du
f
{
g
(
t
)}
F
(
s
)
2
+1)) = 1/(s
–as
–as
L{f(t)} = e
a
(
)
F
s
f
0
–bt
t
(
)
F
u
du
s
1
T
) (
f
t
sT
0
e
f
) (
t
lim
[
s
F
s
*
)(
)}
g
t
G
(
s
)
2
3
2
-s
+s-1).
F(s).
st
) (
.
t
e
dt
L{f(a t)} = (1/a) F(s/a).
f(t)} = F(s+b).
.
st
.
e
dt
(
s
)].
+1).
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