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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Tutorial slides on Python.
%
% Author: FOSSEE
% Copyright (c) 2009, FOSSEE, IIT Bombay
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Taken from Fernando's slides.
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\usepackage[scaled=.95]{helvet}
\definecolor{darkgreen}{rgb}{0,0.5,0}
\usepackage{listings}
\lstset{language=Python,
basicstyle=\ttfamily\bfseries,
commentstyle=\color{red}\itshape,
stringstyle=\color{darkgreen},
showstringspaces=false,
keywordstyle=\color{blue}\bfseries}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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}
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