I was musing the other day on whether it would be easier to teach calculus using O notation. Coincidentally, today I just came across a posted by Alexandre Borovik quoting a letter that Donald Knuth wrote to the Notices of the AMS in 1988 advocating exactly that.

Have you seen Keisler’s book that tries to teach calculus with a nonstandard model of the reals?

I looked at it a bit. I wonder what kind of success Keisler has with it. He does seem to talk a little bit about the metamathematics, which students might find intimidating. Though epsilon-delta is pretty intimidating, so maybe its a wash.

It is much easier to teach calculus with epsilons and deltas.

It is, however, not easier for the students.