Studying Mathematics Thread

[polymath257]

Cauchy did his stuff in the early part of the 19th. By mid-century, the epsilon-delta definition was standard among mathematicians (if not among others).

Some final touches, apparently, a century ago:

Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes back to Bolzano who, in 1817, introduced the basics of the epsilon-delta technique to define continuous functions. However, his work was not known during his lifetime (Felscher 2000). Cauchy discussed variable quantities, infinitesimals, and limits and defined continuity of y = f ( x ) {\displaystyle y=f(x)} by saying that an infinitesimal change in x necessarily produces an infinitesimal change in y in his 1821 book Cours d'analyse, while (Grabiner 1983) claims that he only gave a verbal definition. Weierstrass first introduced the epsilon-delta definition of limit in the form it is usually written today. He also introduced the notations lim and limx→x0 (Burton 1997).

The modern notation of placing the arrow below the limit symbol is due to Hardy in his book A Course of Pure Mathematics in 1908 (Miller 2004).

I lament the fact, though, that many modern calculus texts no longer have a separate, concluding chapter on ODEs.  A step backward in my opinion.

And conic sections appear to have been eliminated from many curricula. Another sad fact.