Problem 4. (. Recall that the convolution of f and g is defined as (S * 9)(t) = 1(2 f(P)g(t – p) dp. Let f(t) = e-2t and g(t) = e". • Evaluate the integral to find the expression for f *g and take the Laplace transform of this expression. Verify that C{f * g} that you found is equal to L{f}L{g}.
Problem 4. (. Recall that the convolution of f and g is defined as (S * 9)(t) = 1(2 f(P)g(t – p) dp. Let f(t) = e-2t and g(t) = e". • Evaluate the integral to find the expression for f *g and take the Laplace transform of this expression. Verify that C{f * g} that you found is equal to L{f}L{g}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 4. (.
Recall that the convolution of f and g is defined as
(S * 9)(t) = S(P)g(t – p) dp.
Let f(t) = e-2t and g(t) = e'.
• Evaluate the integral to find the expression for f * g and take the Laplace transform of
this expression.
Verify that L{f * g} that you found is equal to L{f}L{g}.
Transcribed Image Text:TABLE OF LAPLACE TRANSFORMS
L{1}
n!
L{t"}
sn+1
L {sin (at)}
s2 + a?
L{cos (at)}
s2 + a?
1
S - a
L{d(t – a)}
L{f(t)8(t – a)}
f(a)e-as
F(s – a)
s"Y (s) – s"-'y(0) – ...- y(n-1)(0)
L{f * g}
F(s) G(s)
-as
L{U (t – a)}
L{f(t – a)U (t – a)}
e-a* F(s)
MISCELLANEOUS FORMULAS
yıf
%3D
W
W
Y2
Yn
...
W =
(n)
(n)
(n)
Yn
...
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