A Lost Theorem: Definite Integrals in Asymptotic Setting

Details A Lost Theorem: Definite Integrals in Asymptotic Setting A Lost Theorem: Definite Integrals in Asymptotic Setting

2008-04-19

arxiv.org/abs/0804.3156v1

The American Mathematical Monthly, Volume 115, Number 1, January 2008

Mathematics

Classical Analysis and ODEs

Scientific paper

We present a simple yet rigorous theory of integration that is based on two axioms rather than on a construction involving Riemann sums. With several examples we demonstrate how to set up integrals in applications of calculus without using Riemann sums. In our axiomatic approach even the proof of the existence of the definite integral (which does use Riemann sums) becomes slightly more elegant than the conventional one. We also discuss an interesting connection between our approach and the history of calculus. The article is written for readers who teach calculus and its applications. It might be accessible to students under a teacher's supervision and suitable for senior projects on calculus, real analysis, or history of mathematics.

Affiliated with

Also associated with

No associations

Rating

A Lost Theorem: Definite Integrals in Asymptotic Setting does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Lost Theorem: Definite Integrals in Asymptotic Setting, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Lost Theorem: Definite Integrals in Asymptotic Setting will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-652006