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diff --git a/presentations/ode.tex b/presentations/ode.tex index 655a58f..db2c1d5 100644 --- a/presentations/ode.tex +++ b/presentations/ode.tex @@ -78,13 +78,39 @@ Solving ordinary differential equations. \begin{block}{Prerequisite} \begin{itemize} \item Understanding of Arrays. - \item Python functions. - \item lists. + \item functions and lists \end{itemize} \end{block} \end{frame} \begin{frame}[fragile] +\frametitle{Solving ODEs using SciPy} +\begin{itemize} +\item Let's consider the spread of an epidemic in a population +\item $\frac{dy}{dt} = ky(L-y)$ gives the spread of the disease +\item L is the total population. +\item Use L = 25000, k = 0.00003, y(0) = 250 +\end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{ODEs - Simple Pendulum} +We shall use the simple ODE of a simple pendulum. +\begin{equation*} +\ddot{\theta} = -\frac{g}{L}sin(\theta) +\end{equation*} +\begin{itemize} +\item This equation can be written as a system of two first order ODEs +\end{itemize} +\begin{align} +\dot{\theta} &= \omega \\ +\dot{\omega} &= -\frac{g}{L}sin(\theta) \\ + \text{At}\ t &= 0 : \nonumber \\ + \theta = \theta_0(10^o)\quad & \&\quad \omega = 0\ (Initial\ values)\nonumber +\end{align} +\end{frame} + +\begin{frame}[fragile] \frametitle{Summary} \begin{block}{} Solving ordinary differential equations |