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     2 %Tutorial slides on Python.

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     4 % Author: FOSSEE 

     5 % Copyright (c) 2009, FOSSEE, IIT Bombay

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    58 % Title page

    59 \title{Python for Scientific Computing: Ordinary Differential Equation}

    60 

    61 \author[FOSSEE] {FOSSEE}

    62 

    63 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

    64 \date{}

    65 

    66 % DOCUMENT STARTS

    67 \begin{document}

    68 

    69 \begin{frame}

    70   \maketitle

    71 \end{frame}

    72 

    73 \begin{frame}

    74   \frametitle{About the Session}

    75   \begin{block}{Goal}

    76 Solving ordinary differential equations.

    77   \end{block}

    78   \begin{block}{Prerequisite}

    79     \begin{itemize}

    80     \item Understanding of Arrays.

    81     \item functions and lists

    82     \end{itemize}    

    83   \end{block}

    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 = 250000, 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}

   111 \end{frame}

   112 

   113 \begin{frame}[fragile]

   114   \frametitle{Summary}

   115   \begin{block}{}

   116     Solving ordinary differential equations

   117   \end{block}

   118 \end{frame}

   119 

   120 \begin{frame}

   121   \frametitle{Thank you!}  

   122   \begin{block}{}

   123   This session is part of \textcolor{blue}{FOSSEE} project funded by:

   124   \begin{center}

   125     \textcolor{blue}{NME through ICT from MHRD, Govt. of India}.

   126   \end{center}  

   127   \end{block}

   128 \end{frame}

   129 

   130 \end{document}