September 10th, 2014, 02:11 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, 05:03 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, 06:29 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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convolution, laplace, theorem 
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