Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 18 (2023), 27 -- 48

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DOUBLE CALCULUS

Patrik Lundström

Abstract. We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by Bögel [1, 2], 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.

2020 Mathematics Subject Classification: 26A24, 26A42,26B15
Keywords: continuous function; differentiable function; Riemann integral; the fundamental theorem of calculus

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Patrik Lundström
Department of Engineering Science, University West,
SE-46186 Trollhättan, Sweden.
e-mail: patrik.lundstrom@hv.se

http://www.utgjiu.ro/math/sma