\begin{frame} \frametitle{Mathematical Models} \begin{block}{} A \emph{mathematical model} is a mathematical description of a real-world phenomenon. \end{block} \vspace{-2ex} \pause \begin{center} \begin{tikzpicture}[default,inner sep=1mm] \node[align=center,fill=cblue!10,draw=cdblue!20] (world) {Real-world\\problem}; \pause \node[align=center,fill=cred!10,draw=cdred!20,r=world,xshift=18mm] (model) {Mathematical\\model}; \draw[thick,->] (world) -- node[pos=.5,above] {1} (model); \pause \node[align=center,fill=cgreen!10,draw=cdgreen!20,r=model,xshift=18mm] (conclusions) {Mathematical\\conclusions}; \draw (model) -- node[above] {2} (conclusions); \pause \node[align=center,fill=orange!10,draw=orange!80!black!20,r=conclusions,xshift=18mm] (predictions) {Real-world\\predictions}; \draw (conclusions) -- node[above] {3} (predictions); \pause \draw (predictions) |- ++(0,-1cm) -| node[above,xshift=43.5mm] {4} (world); \end{tikzpicture} \end{center}\vspace{-1ex} \begin{enumerate} \item<3-> Formulate\\ \textcolor{gray}{Identify independent \& dependent variables, simplify and obtain equations (possibly guessing from measurements).} \item<4-> Solve\\ \textcolor{gray}{Apply mathematics such as calculus to derive conclusions.} \item<5-> Interpret\\ \textcolor{gray}{Interpret the model conclusions to predict the real-world.} \item<6-> Test\\ \textcolor{gray}{Compare predictions with reality (revise model if needed).} \end{enumerate} \end{frame}