deletions | additions       diff --git a/Nonlinear irreversible kinetics.tex b/Nonlinear irreversible kinetics.tex  index 38caf61..2cca496 100644  --- a/Nonlinear irreversible kinetics.tex  +++ b/Nonlinear irreversible kinetics.tex 
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From the survival function, we define the time-dependent rate coefficient through an appropriate time derivative depending on the total order of reaction. For first-order irreversible decay reactions, $A\to \textrm{products}$ and $i=1$, the rate law defines the time-dependent rate coefficient  \begin{equation}  k_1(t) \equiv\frac{-d\ln S_1(t)}{dt}  \end{equation}  In traditional kinetics, the rate coefficient irreversible decay is assumed constant, in which case $k(t)\to\omega$. We define $k(t)$ from the appropriate survival function and rate law  \begin{equation}  k_i(t) \equiv \frac{d}{dt}\frac{1}{S(t)^{i-1}}\quad\quad\textrm{for}\quad i=2,3,\ldots. \begin{cases}  \frac{-d\ln S_1(t)}{dt} & \text{if } i = 1 \\  \frac{d}{dt}\frac{1}{S(t)^{i-1}} & \text{if } i \geq 2  \end{cases}  \end{equation}