From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Thu, 15 Aug 1996 10:16:22 -0500 (CDT)
Hi all-
I am now prepared for the first day of class on 8/26. The
students meet on 8/19, but I'll be off on a previously planned trip
(lunch reunion in Montana after a 55 year absence), so I've had
to get the first 2 weeks pinned down.
I'm stuck with a standard text: Anton. It is pompously
nauseating, in my humble opinion.
Yes, Hughes-Hallett is a great improvement, but leaves much
to be desired. The approach is linear:
First we review all there is to know about functions;
Next we introduce the derivative and do all the derivatives.
Now we can do integration.
................................
This is all very anti-Arons, who belabors the important point that
learning math/physics is a very non-linear process. One has to
circle back and see the same concept from many different angles.
I'm following the general approach that I gleaned from The Mechanical
Universe (which is due to Tom Apostol - I hope to see his calculus
book shortly). Briefly - we look at simple curves and introduce
the notion of "limit". Next we do some algebra with polynomials
and quickly get to the limit y->0 of [(x+y)^n -x^n]/y, in the context
of tangents to curves (and average and instantaneous velocities).
More complicated functions are discussed later in relevant
contexts.
I'll try to get a site set up where anyone interested can
download my weekly newsletter to the class.
Regards,
Jack