Double calculus
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 class...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2023-04-01
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| Series: | Surveys in Mathematics and its Applications |
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| Online Access: | https://www.utgjiu.ro/math/sma/v18/p18_03.pdf |
| Summary: | 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. |
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| ISSN: | 1843-7265 1842-6298 |