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From: OsherD on 4 Jan 2010 23:51
From Osher Doctorow

Although t is a dummy variable in I...dt, when I goes from a to tau, t
"traverses Memory". This is clearer in Wikipedia's article on
Volterra equations:

1) f(t) = I K(t,s) x(s) ds (Volterra integral equation of 1st kind,
I...ds integral from s = a to s = t)
2) x(t) = f(t) + I K(t,s) x(s)ds, (Volterra integral equation of 2nd
kind, I...ds integral from s = a to s = t)

Here K(t, s) is called the kernel, and for convolution equation K(t,
s) = K(t - s). Here the fact that s is before t and up to t is
rather clearly shown. There are differences in what is given versus
what is to be solved for. For example, in (1) f is given and K(t, s)
also, and x(s) is to be solved for.

Osher Doctorow
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