My Math Forum Convolution Theorem- Laplace

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 September 10th, 2014, 01:11 PM #1 Newbie   Joined: Sep 2014 From: USA Posts: 1 Thanks: 0 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!
 September 11th, 2014, 04:03 AM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus It is a trivial change of variables. For t=Ïƒ+Ï„, $\mathbb{d}t=\mathbb{d}\sigma$ and for Ïƒ=0 t=Ï„ and as $\sigma \to\infty$ you get $t\to\infty$.
 September 11th, 2014, 05:29 AM #3 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus 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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