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  "body": "\n## Summary\n\nThe Heaviside operational calculus is the formal method of Oliver Heaviside for linear differential equations, developed for electrical circuits.\nThe derivative $d/dt$ is written as a symbol $p$.\nThe response of a system to a unit step input is written as a function of $p$ applied to the step.\nThis expression is then expanded and interpreted by fixed rules.\nThe method gave correct answers long before it was justified; the [[Laplace transform|0V49JEZW06]] and the [[Bromwich integral|5KNAXNHRY6]] later explained why.\n\n## Explanations\n\n### L1 human\n\nHeaviside treated \"differentiate\" as a letter $p$ that can be multiplied, divided and expanded like a number.\nDividing by $p$ means integrating from time $0$.\nA circuit switched on at time $0$ is then described by a fraction in $p$, and expanding that fraction gives the current or voltage as a function of time.\nFor example, the expression $1/(1 - a/p)$ applied to the unit step expands to $1 + a t + a^2 t^2/2 + \\cdots = e^{at}$.\n",
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