Double calculus

Abstract

We present a streamlined, slightly modified version, in the two-variable 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 many two-variable extensions of 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.

Keywords

• continuous function
• differentiable function
• riemann integral
• the fundamental theorem of calculus