From: bobm@Ingres.COM (Bob McQueer)
Newsgroups: alt.folklore.urban
Subject: Re: Why is calculus so feared?
Date: 8 Apr 92 19:04:33 GMT

>         I can't give a good example, I just think that calculus doesn't
> "make sense"..  As hard as I try, it will not become obvious to me.
> That doesn't mean I can't DO it, to some degree, I just don't like doing
> something I don't understand.
> 
>         For example, integrating X to get X^2/2 seems "magical".. And saying
> it's the "area under the curve" is just a hand-waving "explanation".. Actually
> it's not an explanation at all, it's something else it _happens_ to be.

I would suggest that calculus is feared precisely because it is so often
mistaught as a magical "cookbook".  I applaud you for not being happy with
this situation.  I remember all too well from my days as a grad assistant
that most students do not fall into this category, and are more than happy
to be given little recipes to follow without understanding anything about them.

>         Explaining the sum of all of the little boxes whose width gets
> infinitively small gives me a headache! (just kidding)
> 
>         Unfortunately, basically everything in science in college has to
> DO with calculus, making those subjects all the more difficult.

And unfortunately, from your point of view, the practical use of calculus
in the sciences involves making use of the "recipes", rather than performing
Reimann sums to obtain your integral.

It's a fact of life that the practical application of calculus to engineering
and scientific disciplines is important enough that the concepts have to
be taught to students early on, and at a level where a rigorous theoretical
development of real analysis is not practical.

This does NOT say that decent non-rigorous or physical justifications for why
you are doing what you are doing in a freshman calculus course cannot be
offered.  And they should be.

And note that I said the CONCEPTS, not the techniques.  In the real world,
if one understands what an integral is for, and one wishes to calculate
a non-obvious one, handbooks are referred to, or numerical techniques applied.
Certainly, one must learn the basic forms and the basic techniques, but
spending hours applying parts umpty-ump times misses the point.

> ...and took calculus as a senior in high
> school. (Retook it in college since I thought I would understand it more..
> nope)

I DIDN'T take it in high school (not offered), but before I started college
I read a rather good little book called "Inductive Calculus" which developed
basic calculus through discussions of rates of change of functions describing
position and velocity.  I would suggest that the laws of motion provide one
of the best avenues for justifying what you are doing in calculus.  I would
also suggest that a really thorough grounding in analytic geometry is much
more valuable than a cookbook calculus course.

>         I guess calculus is just my major "roadblock".  I am interested in
> chaos and other mathematical subjects that are "higher" than calculus, but
> I'm not taking rigorous classes on those subjects...

Do it.  Eventually, if you take a real "real analysis" course, you'll go back
to square one and actually justify the magic that you learned in calculus.
And hang in there through any differential equations course you might wind
up in, which will likely be even more cookbook.
Xref: sparky alt.folklore.urban:12334 alt.folklore.science:1444