Gordon Couger writes

Computers do away with the need for some calculus. You can just work it out
the long way.

Sure, and that's true of many real life problems.
However if you don't understand the concept of calculus then you are
doing it by rote. Further it's easy to simplify and find an analytic
solution that should be close to the answer to check that your result
looks plausible.

One engineer was trying to find the volume of a stream
profiles at different levels with a computer program. That is a classic area
under a curve problem and she couldn't covert it to code. Since the data was
on a X, Y data it was all straight lines. Each section of the stream could
just be solve using the area of a triangle added to the are of he rectangle
above it. When summed up in a recursive function it took about a half page
of code and a hour to show her how to do it.

Indeed. The very same method that, taken to the limit, is used to prove
integration.

Hmm, I can't quite see why recursion is needed if I understand the
problem as stated.

I doubt she understood recursion but she did get the point about simplifying
the problem.

Quite. Mindless following by rote using tools you don't understand often
results in someone getting cut.

For an engineer anything difficult enough to require calculus has a look up
table anyway

In 8 years of solving problems for engineers I never used calculus once.
Maybe they could solve the ones that needed calculus and just brought me the
hard ones.

It's more than that, often. Frequently simple calculus is used to
generate the basic cell, which is then used numerically for the real
(and thus often tedious, analytically) life problem.

--
Oz
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