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%Tutorial slides on Python.

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% 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}