23-9 Fernando Marques de Almeida Nogueira

Calculus ++ Generalized Differential and Integral Calculus and Heisenberg s Uncertainty Principle (1649K, pdf) 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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