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September 10th, 2014, 02:11 PM   #1
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Convolution Theorem- Laplace

This is my first post so forgive me if I'm not very clear. I'm attempting to understand the convolution theorem of the laplace transform,

http://mathfaculty.fullerton.edu/mat...nTheorem.1.pdf

but can't seem to understand why the limit of integration is changed from (0, inf) to (T, inf), and then again from (T, inf) to (zero, t).

Any help would be greatly appreciated!
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September 11th, 2014, 05:03 AM   #2
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It is a trivial change of variables. For t=σ+τ, $\mathbb{d}t=\mathbb{d}\sigma$ and for σ=0 t=τ and as $\sigma \to\infty$ you get $t\to\infty$.
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September 11th, 2014, 06:29 AM   #3
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Then for the next change of variables, notice the boundaries of the wedge. $0\leq \tau\leq t$ and $0\leq t <\infty$.
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