deletions | additions       diff --git a/Intro1.tex b/Intro1.tex  index 07c35c2..9c69a1d 100644  --- a/Intro1.tex  +++ b/Intro1.tex 
...
The most important piece in extending current theory to higher order irreversible decay is determining the time dependent rate coefficient, which is dependent on the order of reaction. The statistical length and divergence are both functions of the time dependent rate coefficient.  \begin{equation}  \mathcal{L}(\Delta{t})^2=\left[\int_{t_i}^{t_f}k(t)dt\right]^2 \mathcal{L}(\Delta{t})^2 = \left[\int_{t_i}^{t_f}k(t)dt\right]^2  \end{equation}  \begin{equation}  \frac{\mathcal{J}(\Delta{t})}{\Delta{t}}=\int_{t_i}^{t_f}k(t)^{2}dt \frac{\mathcal{J}(\Delta{t})}{\Delta{t}} = \int_{t_i}^{t_f}k(t)^{2}dt  \end{equation}  The inequality between the statistical length and divergence can be shown in two different ways  \begin{equation}  \mathcal{L}(\Delta{t})^2\leq \mathcal{J}(\Delta{t}) \end{equation}  \begin{equation}  \mathcal{J}(\Delta{t})-\mathcal{L}(\Delta{t})^2\geq 0 \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.   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 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. The survival function is simply a measure of a the cocentration of species at some time compared to its initital concentration.  \begin{equation}  S(t)=\frac{[A]_t}{[A]_0} S(t) = \frac{[A]_t}{[A]_0}  \end{equation}  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) \frac{-d\ln S(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 $n^{th}$ order integrated rate law is