Differentiation operator p

Summary

In operational calculus, $p$ denotes the operator $d/dt$ that sends a function of time to its derivative. It is treated as an algebraic symbol: one forms polynomials and fractions in $p$, and $1/p$ is integration from $0$. Because $p$ undoes integration but integration does not quite undo $p$, initial values appear in the rules, as in $p^{-1} p f = f - f(0)$.