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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Tutorial slides on Python.
%
% Author: FOSSEE
% Copyright (c) 2009, FOSSEE, IIT Bombay
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title page
\title{Python for Scientific Computing: Ordinary Differential Equation}
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date{}
% DOCUMENT STARTS
\begin{document}
\begin{frame}
\maketitle
\end{frame}
\begin{frame}
\frametitle{About the Session}
\begin{block}{Goal}
Solving ordinary differential equations.
\end{block}
\begin{block}{Prerequisite}
\begin{itemize}
\item Understanding of Arrays.
\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 = 250000, 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
\end{block}
\end{frame}
\begin{frame}
\frametitle{Thank you!}
\begin{block}{}
This session is part of \textcolor{blue}{FOSSEE} project funded by:
\begin{center}
\textcolor{blue}{NME through ICT from MHRD, Govt. of India}.
\end{center}
\end{block}
\end{frame}
\end{document}
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