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Topic: symbol manipulation
Replies: 7   Last Post: Nov 12, 1997 7:32 PM

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Joshua Zucker

Posts: 710
Registered: 12/4/04
symbol manipulation
Posted: Nov 7, 1997 2:26 PM
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It seems that even at Caltech, most students come in not knowing how
to use an integral as accumulator (e.g. to calculate a moment of
inertia in physics) and the caltech freshman calculus course doesn't

To quote my friend Sanjoy Mahajan, physics TA there:
Currently, you can just forget about using calculus. Most of the
students don't know what an integral is, even if they recognize
the symbols. (The Math 1 class is no help, it's the same as 43H,

[43H is Stanford's freshman honors calculus course, aimed at training
people in theoretical math, using books with minimal if any connection
to applications; in fact, their idea of an "application" is when you
actually *evaluate* an integral in, say, three-dimensional Euclidean
space, as opposed to talking about integrals in more abstract ways.
And now back to the quote...]

where you mostly integrate notation, and forget any math you might
have known.) So they don't know how to set up an integral, even
if they can "do an integral". When you teach integration, do you
use examples like CM, or moment of inertia?

Anyway, I thought you'd like to know that good teachers at Caltech
feel the same frustrations with symbol-manipulation-focused calculus
as a lot of the good teachers on this list, and that the integral as
accumulator idea is one that they want to see emphasized too.

--Joshua Zucker

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