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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 : Solving Equations}

\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}

Using arrays to find solutions and roots or equations.

  \end{block}

  \begin{block}{Prerequisite}

    Understanding of Arrays.

  \end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Solution of equations}

Consider,

  \begin{align*}

    3x + 2y - z  & = 1 \\

    2x - 2y + 4z  & = -2 \\

    -x + \frac{1}{2}y -z & = 0

  \end{align*}

\end{frame}

\begin{frame}[fragile]

\frametitle{Scipy Methods - \typ{roots}}

\begin{itemize}

\item Calculates the roots of polynomials

\item To calculate the roots of $x^2-5x+6$ 

\end{itemize}

\begin{lstlisting}

  In []: coeffs = [1, -5, 6]

  In []: roots(coeffs)

  Out[]: array([3., 2.])

\end{lstlisting}

\vspace*{-.2in}

\begin{center}

\includegraphics[height=1.6in, interpolate=true]{data/roots}    

\end{center}

\end{frame}

\begin{frame}[fragile]

\frametitle{Scipy Methods - \typ{fsolve}}

\begin{small}

\begin{lstlisting}

  In []: from scipy.optimize import fsolve

\end{lstlisting}

\end{small}

\begin{itemize}

\item Finds the roots of a system of non-linear equations

\item Input arguments - Function and initial estimate

\item Returns the solution

\end{itemize}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Summary}

  \begin{block}{}

    \begin{itemize}

    \item Solving linear equations

    \item Finding roots

    \item Roots of non linear equations

    \item Basics of Functions

    \end{itemize}

  \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}