deletions | additions       diff --git a/Intro1.tex b/Intro1.tex  index d124d6f..a7896d6 100644  --- a/Intro1.tex  +++ b/Intro1.tex 
...
\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}  \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)   \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 $n^t{h}$  order integrated rate law is is, where $A+nA\rightarrow B$.  \begin{equation}  [A_t]=\frac{[A_0]}{1+\omega t[A_0]} \frac{1}{[A_t]^{n-1}}=\frac{1}{[A_0]^{n-1}}+(n-1)\omega t  \end{equation}  The second order From the integrated rate law, we get the  survival functionis  \begin{equation}  S(t)=\frac{[A_t]}{[A_0]}=\frac{1}{1+\omega t[A_0]} S(t)=\frac{[A_t]}{[A_0]}\sqrt[n-1]{\frac{1}{1+(n-1)\omega t[A_0]^{n-1}}}  \end{equation}  Fromthis survival function, taking the inverse of  the survival function and then the time derivative yields function,  the time dependent rate coefficient. coefficient is  \begin{equation}  k(t)=\left(\frac{dS(t)^{-1}}{dt}\right) k(t)=(\frac{d\frac{1}{(S(t)^{n-1)}}}{dt})  \end{equation}  The same can be derived for $n^{th}$ Taking our definitions of the integrated rate law, survival function, and time dependent rate coefficient, we are able to apply them to to second  order reactions, where $A+nA\rightarrow B$. irreversible decay.  The integrated rate law of these reactions in second order  is \begin{equation}  \frac{1}{[A_t]^{n-1}}=\frac{1}{[A_0]^{n-1}}+(n-1)\omega t [A_t]=\frac{[A_0]}{1+\omega t[A_0]}  \end{equation}  From the integrated rate law, we get the The second order  survival function is  \begin{equation}  S(t)=\frac{[A_t]}{[A_0]}\sqrt[n-1]{\frac{1}{1+(n-1)\omega t[A_0]^{n-1}}} S(t)=\frac{[A_t]}{[A_0]}=\frac{1}{1+\omega t[A_0]}  \end{equation}  From the this  survival function, taking the inverse of the survival function and then the time derivative yields  the time dependent rate coefficient is coefficient.  \begin{equation}  k(t)=(\frac{d\frac{1}{(S(t)^{n-1)}}}{dt}) k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)  \end{equation}  When it comes to mixed second order reactions, the rate law does not allow a survival function to be obtained for the process because the rate law only allows the survival function of one reactant to be looked at. The rate law of a mixed second order reaction is  \begin{equation}  \int\frac{dx}{([A_0]-x)([B_0]-x)}=k(t)