[FOM] Infinitesimal calculus
Lawrence Stout
lstout at iwu.edu
Tue May 26 10:15:25 EDT 2009
I teach at a college where all of our calculus courses either do
delta-epsilon or the sequence approach to limits carefully. I'd say
that the biggest problem is that high school assumed that the
students didn't need to know any theory and in particular take any
care with definitions, but only learn technique. I've also taught
our senior level real analysis course and a course on infinitesimal
calculus which considered both synthetic differential geometry (which
is intuitionistic) and non-standard analysis. While all of these
approaches pose a hurdle for the students, I found they had least
trouble with the synthetic differential geometry approach found in
Bell's book and in the writings of Kock, Reyes, and Dubuc. One of
the physicists here also found that book intuitive and useful.
More information about the FOM
mailing list