Martin Brown wrote:
On 06/02/2013 22:14, tuinkabouter wrote:
On 2/6/2013 4:51 PM, Tim Wescott wrote:
On Wed, 06 Feb 2013 13:29:16 +0000, Bob Masta wrote:

On Wed, 06 Feb 2013 07:56:07 +0000, Martin Brown
wrote:


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.


I recall struggling through Diffy-Q, which was widely regarded as a "bag
of tricks" subject... you just had to figure out which trick to pull out
of the bag for each special case.

Then next term came Laplace Transforms, where we learned that everything
that needed doing could be done with simple algebra via Laplace... all
that Diffy-Q torture had been just for background information and
building character!

Using the Laplace transform is just a really versatile trick for
approximately solving real-world problems. Here's the reasoning that you
should keep in mind whenever you use it (or the z transform):

1: All real-world systems are nonlinear and time varying.
2: The Laplace transform only works on systems that are linear and time-
invariant.
3: Thus, I cannot use the Laplace transform to solve this problem.
4: But I can come _close_ by linearizing this here system
5: And now I can use Laplace!

This works great a whole lot of the time -- but it doesn't always, and
engineers who are steeped in Laplace (or the z transform) tend to forget
that they've skipped over steps 1-3, and did 4 without questioning why,
or when it is not valid to do so.

These discussion brings back some memories.
I hope i don't have bad dreams tonight.

Following to Laplace we where tortured with Hilbert transformations.

After university i never had to solve a differential- or integral
equations.

I still have serious hatred of Green's functions arising from that
particular course. Lucky we no longer do it analytically any more.


I recall the materials course where the prof explained everything using
tensor calculus. Unfortunately, nobody had previously bothered to teach us
tensor calculus. All the lectures were pure gibberish. I'm not at all sure
how I passed that course.