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15 relations: Applied mathematics, Cauchy formula for repeated integration, Derivative, Differential operator, Fourier transform, Fractional calculus, Fractional-order integrator, Function (mathematics), Grünwald–Letnikov derivative, Integral transform, Laplace transform, Periodic function, Riemann–Liouville integral, Semigroup, Weyl integral.
Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Cauchy formula for repeated integration
The Cauchy formula for repeated integration, named after Augustin Louis Cauchy, allows one to compress n antidifferentiations of a function into a single integral (cf. Cauchy's formula).
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Fractional calculus
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator and of the integration operator and developing a calculus for such operators generalizing the classical one.
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Fractional-order integrator
A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative (usually called a differintegral) of an input.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Grünwald–Letnikov derivative
In mathematics, the Grünwald–Letnikov derivative is a basic extension of the derivative in fractional calculus that allows one to take the derivative a non-integer number of times.
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Integral transform
In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
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Riemann–Liouville integral
In mathematics, the Riemann–Liouville integral associates with a real function ƒ: R → R another function Iαƒ of the same kind for each value of the parameter α > 0.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Weyl integral
In mathematics, the Weyl integral is an operator defined, as an example of fractional calculus, on functions f on the unit circle having integral 0 and a Fourier series.
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Basic properties of the differintegral, Basic rules of differintegration, Differintegration, Differintegration of some elementary functions, Fractional integral, Fractional integration, Fractional integration and differentiation.
