Re: Physics Test and Integration

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 8:15 -0600 1/31/02, Tina Fanetti wrote:
> I was wondering.  I am teaching calc-based intro physics.  Most of th=
> e students are in Calc 2.  So they don't know much integration beside=
> s the basics.
>
> When you give them tests in electricity and magnetism, how do you han=
> dle the integration?  Do you give them the integrals they need, do yo=
> u "fix" the problems so the integration is basic or do you just tell =
> them to work the problem down to the integral and leave it in integra=
> l form.
>
> I am worried that 1) they will panic, 2) they will miss a method and =
> make the integral harder, 3) I'll screw up and give them a harder pro=
> blem that requires more integration than they know...
>
> I was curious as to how other handle this.=20
I had the same problem when I was teaching this course, and I found
that the best way to do it was just to teach the students the basic
calculus they needed. Really basic. I pointed out that an integral
was just the inverse of a derivative, that there was no analytical
method to solve an integral, except to fiddle around with the
integrand until you got it into a form that you could recognize as
the derivative of a known function, and then I simply stated the
fundamental theorem of integral calculus and told them that the proof
would be forthcoming in their calculus class. We practiced the
technique a while, they generated a small table of integrals, and
that was it. After that they were on their own.

The basic issue is to de-mystify the process. Show them how the
kinematic equations can be written as differential equations--ones
that they have already solved. Point out that in solving differential
equations, one of the standard methods is to guess a solution and try
it out to see if it works, and then walk them through the solution of
a couple of common ones, like a simple RC or RL circuit, and the
simple harmonic motion (RLC) problem.

If they understand that integration is just inverse differentiation,
and differential equations are just a fancy name for equations that
they have already solved, they won't be so likely to panic when they
see one. That should enable them to get past that hurdle, and not be
quite so awed when they see some of the more difficult forms.

Good luck,

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

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