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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}