 239 Fernando Marques de Almeida Nogueira
 Calculus ++ Generalized Differential and Integral Calculus and Heisenberg s Uncertainty Principle
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Mar 9, 23

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Abstract. This paper presents a generalization for Differential and Integral Cal
culus. Just as the derivative is the instantaneous angular coefficient of
the tangent line to a function, the generalized derivative is the instan
taneous parameter value of a reference function (derivator function)
tangent to the function. The generalized integral reverses the general
ized derivative, and its calculation is presented without antiderivatives.
Generalized derivatives and integrals are presented for polynomial, expo
nential and trigonometric derivators and integrators functions. As an
example of the application of Generalized Calculus, the concept of
instantaneous value provided by the derivative is used to precisely deter
mine time and frequency (or position and momentum) in a function
(signal or wave function), opposing Heisenberg s Uncertainty Principle
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