Calculus ++ Generalized Differential and Integral Calculus-Reference-Cited by-同舟云学术

Calculus ++ Generalized Differential and Integral Calculus

Published:2023-08-11 Issue: Volume: Page:
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Author:

Nogueira Fernando Marques de Almeida¹

Affiliation:

1. Juiz de Fora Federal University

Abstract

AbstractThis paper presents a generalization for Differential and Integral Calculus. Just as the derivative is the instantaneous angular coefficient of the tangent line to a function, the generalized derivative is the instantaneous parameter value of a reference function (derivator function) tangent to the function.The generalized integral reverses the generalized derivative, and its calculation is presented without antiderivatives.Generalized derivatives and integrals are presented for polynomial, exponential 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 determine frequency in a function, by means of the Fourier Derivative or Trigonometric Derivators Functions.

Publisher

Research Square Platform LLC

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