Re: teaching "higher" math functions

[John Denker <jsd@MONMOUTH.COM>]

At 07:12 AM 11/30/99 -0500, David Bowman wrote:

>  Explaining higher math functions to students who don't
> know the necessary calculus used in defining those functions in the first
> place could be tricky.

That's true.

Let me point out that the same could be said for lower-math functions like
sines and logarithms.  According to my point of view, there is a difference
between parabolas and sine waves, but a much slighter difference between
things like sine waves, Bessel functions, and elliptic integrals.

The differences I am talking about have to do with how familiar they are,
and how hard they are to evaluate by hand.  We pretend everyone is able to
multiply by hand (even though many folks can't, and rely on a
calculator).  In contrast, very few people evaluate trig functions by
hand.  They look them up in tables or (these days) use calculators or
PCs.  Elliptic functions just require a better-equipped PC -- a difference
in degree, not a difference in kind.  This can be illustrated by a marginal
case: the error-function Erf().  Some spreadsheet programs implement it,
some don't.

>  My guess would be to demonstrate them via their
> graphs as they are applied to the relevant physical situations.  For
> instance, one could plot the graph of the total distance travelled by a
> planet or comet along its orbital path as a function of time and/or
> orbital longitude.

Right.  That is exactly parallel to the way one should introduce sinusoidal
motion or exponential decay.  After (!) explaining how to get the key ideas
from the graph itself, one can remark that the function comes up in other
contexts, has been given a name, and can be evaluated to high accuracy
using published tables and/or published algorithms.