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Re: Finding zeros.
Posted:
Mar 7, 1997 3:28 PM
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This discussion of pathology is interesting to me.
And long overdue, I think. I deliberately expose
students to the inherent weaknesses of their machines.
I agree with Jerry that we tear down learning by
deliberately laying down pathological examples
as unmarked land mines. I doubt that these sorts
of bizarre functions occur in the real world.
But, shouldn't students be struck with
something like integral(0,10000,e^(-x^2),x) = 0.
Go ahead, try it on your favorite numerical integrator.
Try graphing sin(47x) (or something similar, depending
on screen resolution) ...
Try to find a point of intersection of y1=sin(x) / x and
y2 = 1/x on a TI-8x. Drat, no sign change...
Is there something to *teach* by looking at these sorts of
examples (if that is our honestly stated, up front intent)?
I think so. And, remarkably, many of my own students are
*interested* in seeing their machine screw up! And want to
know *why* it happened.
Mark Howell
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