Double Calculus
Abstract
We present a streamlined, slightly modified version, in the twovariable situation, of a beautiful, but not so well known, theory by Bögel, already from the 1930s, on an alternative higher dimensional calculus of real functions, a double calculus, which includes twovariable 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.08082
 Bibcode:
 2021arXiv210608082L
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  History and Overview
 EPrint:
 21 pages