10 Jun
2010
10 Jun
'10
2:31 p.m.
Tony Duell [ard at p850ug1.demon.co.uk] wrote:
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.
Air resistance is ignored because otherwise the equations become too
complex. In any particular real world example that may or may not
lead to unacceptable errors.
The constant approximation is far less of a problem. The Earth's
radius is what ~6Mm, so even if your height changes by say 60m then
that's less than 1%.
The point is to teach you the simple case so that you understand it
and can move on to the complications later. There won't be a "later"
in A-level maths because there isn't enough time (you have to fit in
the rest of the course and the remaining A-levels).
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.
I don't recall whether I started solving stuff numerically at A-level
or at degree-level, I suspect the latter. However, I do recall that the
point of A-level maths was to teach the basics of calculus and some
of its applications (I didn't cover any of the statistics options in my
course). I could complain that there was no coverage of vector calculus
at A-level and that I had to (horror!) go and find out what it was all
about when I realised that the degree course turned out to be
- use vector calculus (Maxwell's equations or some such)
[weeks later]
- two lectures on vector calculus and what it's all about
I could complain that the basic electronics on my engineering science
course was pretty rudimentary and that the practicals were (in my view)
pretty basic. But there was a lot packed into the course and it
provided a foundation for many different areas. I don't think I could
be trusted to build a bridge now, but if I'd been that way inclined
I would have had enough of a grounding to get my foot in the door
somewhere.
Antonio