Double Calculus
Classical Analysis and ODEs
2021-07-23 v6 History and Overview
Abstract
We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by B\"{o}gel, already from the 1930s, on an alternative higher dimensional calculus of real functions, a double calculus, which includes two-variable extensions of many classical results from single variable calculus, such as Rolle's theorem, Lagrange's mean value theorem, Cauchy's mean value theorem, Fermat's extremum theorem, the first derivative test, and the first and second fundamental theorems of calculus.
Cite
@article{arxiv.2106.08082,
title = {Double Calculus},
author = {Patrik Lundström},
journal= {arXiv preprint arXiv:2106.08082},
year = {2021}
}
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21 pages