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\centerline{Workshop \#1}
\centerline{APM 115: mathematical modeling}
\begin{enumerate}
\item Introduction to Matlab
\item Consider the growth rate of the logistic equation $r(N)$ plotted
  in (a).  You may want to start from the sample Matlab program
  workshop01.m. 
  \begin{itemize}
  \item Write an analytic expression for this growth rate as well
  as for the right hand side of the logistic equation,
  $\dot{x}=f(N)=r(N)*N$.
  \item Plot both using Matlab
  \item Use the graphics method to solve for the fixed points and
    their stability.
  \item Use ode45 in Matlab to solve for N(t) starting an initial
    condition that is close but not equal to zero.  (use the program
    given to you as a starting point).
  \end{itemize}
\item Repeat all the above items for the growth rate shown in (b).
\end{enumerate}

  \begin{figure}[h] %  figure placement: here, top, bottom, or page
     \centering
     \includegraphics[width=4in]{Figures/workshop01.jpg} 
     \caption{two logistic growth rates}
     \label{fig:example}
  \end{figure}

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