I am trying to understand how to determine the limits of integration
of convolution integrals for simple instantaneous unit hydrographs
(IUH).  I am looking for EXCELLENT resources because my teacher sucks.
 EXCELLENT internet resources work, or EXCELLENT very basic books on
the subject.

Example of problem I'm tying to solve:  rain falls at a certain rate
for a certain time on an impermeable smooth surface such as a section
of a circle.  The rain runs off at a certain linear velocity toward
the "center" of the section of the circle:  What is the IUH of the
runoff at various times after the rain begins?

I understand the how to integrate, but there is a "time shift" between the
time variables "t" and "Tao," and you've got to get the limits of
integration right.

Again, I'm not looking for someone to solve the problem, just THE BEST
resources that explain really well how you go about determining
the limits of integration.

Hi thanks for the question, 

try this link, 
hope that helps
http://www.jhu.edu/~signals/convolve/index.html