deletions | additions       diff --git a/Intro1.tex b/Intro1.tex  index f739c90..012c980 100644  --- a/Intro1.tex  +++ b/Intro1.tex 
...
\end{equation}  The second form of the inequality is the most useful, as the difference in $\mathcal{J}(\Delta t)$ and $\mathcal{L}(\Delta t)^2$ measures the variation in the rate coefficient. When the difference between these two quantities is zero, the rate coefficient is constant.   his inequality is derived from the first order rate law and survival function. In traditional kinetics, irreversible decay is only dependent on one rate coefficient, $\omega$, and the mechanism of the reaction. The rate law of a first order reaction of A irreversibly decaying into B is   \begin{equation}  \frac{-dA}{dt}=\omega[A]  \end{equation}  The mechanism of each irreversible decay reaction may be different. For example, the irreversible decay of A into B may follow second order kinetics, where the rate law is  \begin{equation}  \frac{-dA}{dt}=\omega[A]^2  \end{equation}  The time dependent rate coefficient, k(t), is determined by integrating the rate law of the reaction and forming a survival function from the integrated rate law. From the survival function, the time dependent rate coefficient is determined by taking various time derivatives of the survival function, depending on the total order of reaction. For first order irreversible decay reactions, the time dependent rate coefficient is the negative time derivative of the natural log of the survival function[insert citation]  \begin{equation}  \frac{-dlnS(t)}{dt}=k(t)   \end{equation}  In order to determine the time dependent rate coefficient in higher order reactions, it is useful to use the survival function, but is not necessary. The survival function of any reaction involving any number of the same molecule can be derived using the integrated rate laws of reactions. For example, the second order integrated rate law is 
...
From this survival function, taking the inverse of the survival function and then the time derivative yields the time dependent rate coefficient.  \begin{equation}  k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)=\frac{d}{dt}\left[1+\omega t[A_0]\right]=\omega[A_0] k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)  \end{equation}  This inequality is derived from the first order rate law and survival function. In traditional kinetics, irreversible decay is only dependent on one rate coefficient, $\omega$, and the mechanism of the reaction. The rate law of a first order reaction of A irreversibly decaying into B is   \begin{equation}  \frac{-dA}{dt}=\omega[A]  \end{equation}  The mechanism of each irreversible decay reaction may be different. For example, the irreversible decay of A into B may follow second order kinetics, where the rate law is  \begin{equation}  \frac{-dA}{dt}=\omega[A]^2  \end{equation}  The time dependent rate coefficient, k(t), is determined by integrating the rate law of the reaction and forming a survival function from the integrated rate law. From the survival function, the time dependent rate coefficient is determined by taking various time derivatives of the survival function, depending on the total order of reaction. For first order irreversible decay reactions, the time dependent rate coefficient is the negative time derivative of the natural log of the survival function[insert citation]  \begin{equation}  \frac{-dlnS(t)}{dt}=k(t)   \end{equation} T