  The steady-state approximation (hereafter abbreviated as SSA) consists in
setting $dy/dt=0$, where $y$ denotes the concentration of a short-lived
intermediate subject to first-order decay with a rate constant $k$. The sole
reason for enforcing SSA is to convert the rate equation for $y$ into an
algebraic equation. The conditions under which SSA becomes trustworthy are now
well understood, but a firm grasp of the physical content of the approximation
requires more maturity than few teachers, let alone their students, may be
expected to possess. Furthermore, there is no simple way to gauge the accuracy
of the results derived by imposing SSA. The purpose of this note is to
demonstrate that a better, but equally simple, approximation results if,
instead of setting $dy/dt$ to zero, one substitutes $y(t+\tau)$ for $y+\tau
dy/dt$, where $\tau=1/k$; SSA is a cruder approximation because it neglects the
second term. For systems modelled as damped harmonic oscillators, the "reverse
Taylor approximation" can be extended by retaining one more term in the Taylor
expansion. The utility of the approximation (or its extension) is demonstrated
by examining the following systems: radioactive equilibria, Brownian motion,
dynamic response of linear first- and second-order systems.

General Physics