This little book is especially concerned with those portions of
”advanced calculus” in which the subtlety of the concepts and methods
makes rigor difficult to attain at an elementary level. The approach
taken here uses elementary versions of modern methods found in
sophisticated mathematics. The formal prerequisites include only a term
of linear algebra, a nodding acquaintance with the notation of set
theory, and a respectable first-year calculus course (one which at least
mentions the least upper bound (sup) and greatest lower bound (inf) of a
set of real numbers). Beyond this a certain (perhaps latent) rapport
with abstract mathematics will be found almost essential.

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