HP 48gII User Manual
Page 492
Page 16-14
Now, use ‘(-X)^3*EXP(-a*X)’
` LAP µ. The result is exactly the same.
• Integration theorem. Let F(s) = L{f(t)}, then
• Convolution theorem. Let F(s) = L{f(t)} and G(s) = L{g(t)}, then
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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
2
+1).
Also, ‘EXP(X)’
` LAP. Result, ‘1/(X-1)’, i.e., G(s) = 1/(s-1). Thus, L{(f*g)(t)}
= F(s)
⋅G(s) = 1/(s
2
+1)
⋅1/(s-1) = 1/((s-1)(s
2
+1)) = 1/(s
3
-s
2
+s-1).
• Shift theorem for a shift to the right. Let F(s) = L{f(t)}, then
L{f(t-a)}=e
–as
⋅L{f(t)} = e
–as
⋅F(s).
• Shift theorem for a shift to the left. Let F(s) = L{f(t)}, and a >0, then
• Similarity theorem. Let F(s) = L{f(t)}, and a>0, then L{f(a⋅t)} =
(1/a)
⋅F(s/a).
• Damping theorem. Let F(s) = L{f(t)}, then L{e
–bt
⋅f(t)} = F(s+b).
• Division theorem. Let F(s) = L{f(t)}, then
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