ch3_math.tex
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ch3_math.tex
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			\chapter{Mathematics}
			In this chapter we will see some examples of mathematics.

			Here's an example how to cite.~\cite{alipanahi_predicting_2015}

			\lipsum[1]

			\section{Very important formulas}
			\lipsum[2]

			\begin{equation}\label{eqn:rate_eqns}
			\frac{\textrm{d}}{\textrm{d}t}\left[
			\begin{array}{l}
			P_{\textit{0}} \\
			P_{\textit{1}} \\
			P_{\textit{T}}
			\end{array}
			\right] =
			\left[
			\begin{array}{l}
			\frac{P_{\textit{1}}}{\tau_{\textit{10}}} + \frac{P_{\textit{T}}}{\tau_{\textit{T}}} - \frac{P_{\textit{0}}}{\tau_{\textit{ex}}} \\
			- \frac{P_{\textit{1}}}{\tau_{\textit{10}}} - \frac{P_{\textit{1}}}{\tau_{isc}} + \frac{P_{\textit{0}}}{\tau_{\textit{ex}}} \\
			\frac{P_{\textit{1}}}{\tau_{isc}} - \frac{P_{\textit{T}}}{\tau_{\textit{T}}}
			\end{array}
			\right]
			\end{equation}

			\lipsum[3]


			\begin{equation}\label{eqn:avgfluorescence}
			\bar{I_{f}}(\vec{r})
			= \gamma(\vec{r}) \left(1 - \frac{\tau_{\textit{T}} P_{\textit{T}}^{{eq}}\left(1-\exp \left(-\frac{(T_p - t_p)}{\tau_{\textit{T}}}\right)\right)}{1-\exp\left(-\frac{(T_p - t_p)}{\tau_{\textit{T}}} + k_{\textit{2}} t_p\right)} \times \frac{\left(\exp\left(k_{\textit{2}} t_p\right)-1\right)}{t_p} \right)
			\end{equation}

			\lipsum[3]