Convolution Product
Convolution Product
One of the most common mistake students will commit is
Although it is tempting to assume that this is true, one may easily check
that it is wrong by taking f(t) = t, and g(t) = t. Therefore, a
natural question is: what would 
be
equal to ?
The answer to this question is given by the formula
where
,
is called the convolution product of f(t), and
g(t). The following are some of
the basic properties of the convolution product:
;
;
;
;
.
Example: Find the solution to
Solution: Apply the Laplace transform to get
where 
. Hence,
We then rewrite Y(s) to get
Therefore, we have
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Author: Mohamed Amine Khamsi