On 6/10/10, Tony Duell <ard at p850ug1.demon.co.uk> wrote:
When I was at school doing A levels, the subject
I really hated was
applied maths' (motion of bodies under various forces, projectile
motion, etc). The reason is that it was so _fake_. There wrre so many
unjustified approximations that it is useless in the real world. It was
just a game to get you to solve equations.
"Assume you have a bulldozer of negligible mass"
or
"I have a solution, but it only works for spherical chickens in a vacuum"
etc., etc.
Oh, it was wore thsn that. The projectile motion always invovled a
parabolic trajectory. This assumes not only zero air resistance, but also
uniform gravity acting vertically downwards -- in other words a flat
earth. Which I don't believe in.
There is nothing wrong with approxiamtions, of course. Although Newtonian
mechanics is an approxiation to special relativity, I have no problem
using hte former to work out what will happen to normal-sized objects
moving at normal speeds. What annoyed me about applied maths was the
_major_ approximationnts oyu made, which then resulted in some
nasty-looking equaitons that you had to integrate analyitcally. The point
being that if you'd integrated them numerically, the errors from that
would have been much less than the errors introuced by the
approximations, and becuase the equations _were_ based on approximations
there was little point in fionding he analytic forom of the answer, it
didn't really tell you how the system would really behave.
No it was a silly game to get you to solve equations.
-tony