[FOM] Infinitesimal calculus

[Lawrence Stout]

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.