Generalized Differential and Integral Calculus and Heisenberg Uncertainty PrincipleThis 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 time and frequency (or position and momentum) in a
function (signal or wave function), opposing Heisenberg's Uncertainty
Principle.
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