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Unitary Calculus and Antiunitary or Complectional Calculus: A new type of Calculus
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ISBN13: 9798411279597
Publisher: Independently Published
Pages: 178
Weight: 0.80
Height: 0.38 Width: 8.00 Depth: 10.00
Language: English
Publisher: Independently Published
Pages: 178
Weight: 0.80
Height: 0.38 Width: 8.00 Depth: 10.00
Language: English
The Unitary Calculus treats of local approximations of functions by potential functions, this is, by functions of the form f(x) = cx d, whereas the Differential Calculus allows us to obtain local approximations by affine functions, this is, by functions of the form f(x) = mx + n. The Unitary Calculus allows to evaluate quotients of the form f(b) / f(a), being f a function, whereas the Differential Calculus allows to evaluate differences of the form f(b) - f(a).
The Antiunitary or Complectional Calculus is with respect to the Unitary Calculus what the Integral Calculus is with respect to the Differential Calculus. We will see a strong parallelism between both theories. Whereas in the Integral Calculus we speak about Riemann sums, in the Antiunitary Calculus we speak about of Riemann products, and we need a concept of distance which is compatible with the idea of product, in the same way that the usual concept of distance in R, the absolute value of the difference, is compatible with the idea of sum.
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