Re: numerical methods (was: banning calculators)

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

At 14:13 2002/03/15, Oren Quist wrote:

> My other favorite one is to require an answer with more significant digits
> than their calculator can provide.  e.g. find the square root of 1/(0.98) to
> 13 (or 14 or 15) places.  It's simple to do by expanding it, but students
> hate expansions more than they hate to think.
>
> But, I can't think of any real use of such a calculation other than to show
> students that their calculators cannot do everything for them.

Give them an approximation formula for the probability of tunneling through
a thick, high quantum barrier, such that the probability is e^(- (some
number with a huge absolute value)). Such a formula is given in the quantum
section near the back of, for example, Fundamentals of Physics, extended
version, by Halliday and Resnick; I don't have the exact page reference but
look in the index under tunneling. The calculation, if properly set up,
gives an underflow condition even on calculators that go down to 10^-999.
This forces students to use what they know about logarithms to get the
answer. I don't know if this qualifies as a "real use", but at least they
might get an idea why baseballs don't ordinarily tunnel through block
walls, and simultaneously be forced to make do without their calculators
for at least a portion of the problem. I don't know whether students hate
expansions or logarithms more.

--MB