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Heaviside’s Operator Calculus (2007)
An operational calculus converts derivatives and integrals to operators that act on functions, and by doing so ordinary and partial linear differential equations can be reduced to purely algebraic …
In the end Laplace transforms, easier to use with a more rigorous structure and incorporating the powerful tool of convolution, overtook the operational calculus of Heaviside, and his methods largely fell victim to history. Heaviside took the basic equations for voltage v and current i for a discrete resistance R, capacitance C and inductance L and rewrote them using his operator p, which performed the derivative with respect to time on the function to the right of it (effectively d/dt), as in p·f(t). Heaviside generally treated problems in which a constant voltage is applied to a circuit at time t=0, in other words an impulse (or step function) such as might be encountered as transient signals on cables.
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