84 \end{frame}

    85 

    86 \begin{frame}[fragile]

    87 \frametitle{Solving ODEs using SciPy}

    88 \begin{itemize}

    89 \item Let's consider the spread of an epidemic in a population

    90 \item $\frac{dy}{dt} = ky(L-y)$ gives the spread of the disease

    91 \item L is the total population.

    92 \item Use L = 25000, k = 0.00003, y(0) = 250

    93 \end{itemize}

    94 \end{frame}

    95 

    96 \begin{frame}[fragile]

    97 \frametitle{ODEs - Simple Pendulum}

    98 We shall use the simple ODE of a simple pendulum. 

    99 \begin{equation*}

   100 \ddot{\theta} = -\frac{g}{L}sin(\theta)

   101 \end{equation*}

   102 \begin{itemize}

   103 \item This equation can be written as a system of two first order ODEs

   104 \end{itemize}

   105 \begin{align}

   106 \dot{\theta} &= \omega \\

   107 \dot{\omega} &= -\frac{g}{L}sin(\theta) \\

   108  \text{At}\ t &= 0 : \nonumber \\

   109  \theta = \theta_0(10^o)\quad & \&\quad  \omega = 0\ (Initial\ values)\nonumber 

   110 \end{align}