On 05/02/2013 19:26, Tim Wescott wrote:
On Tue, 05 Feb 2013 12:18:20 -0700, Jim Thompson wrote:

On Tue, 05 Feb 2013 13:16:39 -0600, Tim Wescott
wrote:

And, finally, if you do this a lot with linear, shift-invariant
difference equations, it pays to learn how to use the z-transform. It
simplifies things almost as much as the Laplace transform does for
linear time-invariant differential equations, and makes all of this
folderol much easier to remember.

Yep, It's all coming back to me... guess a solution and prove it fits
:-(

The guy who taught my second term of diff eqs clearly wanted us to
remember this for all time, because he made this a mantra. Nearly every
class meeting he would put some new form of differential equation up on
the board, and he'd say "Now, how do we solve this differential
equation?" then (because we didn't all shout it out in unison) he'd
answer himself: "We guess, and prove that we're right!"

That was 30 years ago. It's stuck with me, so I guess he met his goal in
my case.

I still recall my first serious brush with exotic differential equations
in the freshman year although for different reasons.

The lecturer was an internationally famous astronomer and brilliant
analytical solver of novel differential equations. The snag was that he
could not teach for toffee and merely demonstrated pulling rabbit out of
hat again and again and again. His coursework was impossible.

This particular course was so incomprehensible that after a while the
best of us went to the other stream of maths on group theory since it
was so much easier and the exam questions were likely to be possible to
solve in finite time. Some from the other course which then became badly
overcrowded then went to the ODE course so they could sit down.

Indirectly he probably contributed to the increased use of computers to
solve differential equations as we later moved into research.

--
Regards,
Martin Brown