🚀 go-pugleaf

On Tue, 20 Dec 1994 V064Q5C3@ubvms.cc.buffalo.edu wrote:

> Making the following assumptions:
> 	--the time between measurements is known and stored in the variable
> 		D
> 	--the force at time t is stored in L1
> 	--there are n items in L1, and n is stored in the variable
> 		N
>
> The following "program" will estimate the area under the curve using
 trapizoids

At a glance, the program looks good.  I'd really like to encourage you
all to use this method rather than regression+integration.  After all,
why approximate the data you have before integrating?  Why not integrate
with the actual data?

I also mention this because it is misleading to give students the
impression that there is always a "right" formula out there somewhere.
Often there isn't, or at least it isn't one of the formulas the calculator
will use in approximation.  (I had direct experience with this this term;
I gave data that came from a formula k-k*a^t, with k and a constants.
None of the TI regression modes fits it very well, but some students
tried and crashed.  All this was in a much larger context).

We must be able to cope anyway.  I expect direct numeric integration as
suggested above is much closer to what a field engineer would do, UNLESS
there were strong reason to expect the data points to _very_ closedly FIT
a known type of formula.  You might want to modify the program to do
Simpson's rule, but I think the trapezoid rule is great as it is.

Note that I'm not against regression, just against reflexive regression
use, which some of my students were infected with this past term....
"It's gotta be a polynomial!"  (Yeah, right).


Mark Janeba			(503)370-6123
Dept. of Mathematics		e-mail:  mjaneba@willamette.edu
Willamette University		"Speaking for myself, not the university"
Salem, Oregon 97301-3922 USA