Paul said:
Well I've had a peek at your link and one of my reference books and it
appears this Laplace stuff involves calculus. Algebra's one thing, but
I never got around to studying Leibnitz's little contribution to
science and don't plan to start now. So I guess I'm stuck with the
messy way!
The whole purpose of this 's' domain stuff is actually to *avoid* calculus
(specifically solving differential equations). By solving in the 's' domain,
the problem is reduced to an algebraic one. Note that if you just want
frequency response, or circuit impedance, 's' is simply replaced by 'jw'. No
calculus there -- just a substitution. Solving with 's' is a more complete
solution, in the sense that it includes the transient part. Not only that, it
is notationally simpler too.
If one wants the _complete_ (time domain) response, meaning including the
transients, then 's' is not replaced by 'jw' before performing the
transformation to the time domain. Even though the Laplace Transform is by
definition calculus (an integral to be specific), there exists a big
table/library of canned transforms for the purpose of avoiding calculus. So use
*algebra* to put the 's' domain solution into a recognized canned form. Use the
canned form to convert to the time domain. Voilà, no calculus. The Laplace
Transform is your best friend.