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+% Created 2010-11-11 Thu 02:03
+\documentclass[presentation]{beamer}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{fixltx2e}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{float}
+\usepackage{wrapfig}
+\usepackage{soul}
+\usepackage{textcomp}
+\usepackage{marvosym}
+\usepackage{wasysym}
+\usepackage{latexsym}
+\usepackage{amssymb}
+\usepackage{hyperref}
+\tolerance=1000
+\usepackage[english]{babel} \usepackage{ae,aecompl}
+\usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet}
+\usepackage{listings}
+\lstset{language=Python, basicstyle=\ttfamily\bfseries,
+commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen},
+showstringspaces=false, keywordstyle=\color{blue}\bfseries}
+\providecommand{\alert}[1]{\textbf{#1}}
+
+\title{Getting started with symbolics}
+\author{FOSSEE}
+\date{}
+
+\usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent}
+\begin{document}
+
+\maketitle
+
+
+
+
+
+
+
+
+
+\begin{frame}
+\frametitle{Outline}
+\label{sec-1}
+
+\begin{itemize}
+\item Defining symbolic expressions in sage.
+\item Using built-in constants and functions.
+\item Performing Integration, differentiation using sage.
+\item Defining matrices.
+\item Defining Symbolic functions.
+\item Simplifying and solving symbolic expressions and functions.
+\end{itemize}
+\end{frame}
+\begin{frame}
+\frametitle{Question 1}
+\label{sec-2}
+
+\begin{itemize}
+\item Define the following expression as symbolic
+    expression in sage.
+
+\begin{itemize}
+\item x$^2$+y$^2$
+\item y$^2$-4ax
+\end{itemize}
+
+\end{itemize}
+
+  
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Solution 1}
+\label{sec-3}
+
+\lstset{language=Python}
+\begin{lstlisting}
+var('x,y')
+x^2+y^2
+
+var('a,x,y')
+y^2-4*a*x
+\end{lstlisting}
+\end{frame}
+\begin{frame}
+\frametitle{Question 2}
+\label{sec-4}
+
+
+\begin{itemize}
+\item Find the values of the following constants upto 6 digits  precision
+
+\begin{itemize}
+\item pi$^2$
+\item euler$_{\mathrm{gamma}}$$^2$
+\end{itemize}
+
+\end{itemize}
+
+\begin{itemize}
+\item Find the value of the following.
+
+\begin{itemize}
+\item sin(pi/4)
+\item ln(23)
+\end{itemize}
+
+\end{itemize}
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Solution 2}
+\label{sec-5}
+
+\lstset{language=Python}
+\begin{lstlisting}
+n(pi^2,digits=6)
+n(sin(pi/4))
+n(log(23,e))
+\end{lstlisting}
+\end{frame}
+\begin{frame}
+\frametitle{Question 3}
+\label{sec-6}
+
+\begin{itemize}
+\item Define the piecewise function. 
+   f(x)=3x+2 
+   when x is in the closed interval 0 to 4.
+   f(x)=4x$^2$
+   between 4 to 6.
+\item Sum  of 1/(n$^2$-1) where n ranges from 1 to infinity.
+\end{itemize}
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Solution 3}
+\label{sec-7}
+
+\lstset{language=Python}
+\begin{lstlisting}
+var('x') 
+h(x)=3*x+2 
+g(x)= 4*x^2
+f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x)
+f
+\end{lstlisting}
+
+\lstset{language=Python}
+\begin{lstlisting}
+var('n')
+f=1/(n^2-1) 
+sum(f(n), n, 1, oo)
+\end{lstlisting}
+\end{frame}
+\begin{frame}
+\frametitle{Question 4}
+\label{sec-8}
+
+\begin{itemize}
+\item Differentiate the following.
+
+\begin{itemize}
+\item sin(x$^3$)+log(3x), to the second order
+\item x$^5$*log(x$^7$), to the fourth order
+\end{itemize}
+
+\item Integrate the given expression
+
+\begin{itemize}
+\item x*sin(x$^2$)
+\end{itemize}
+
+\item Find x
+
+\begin{itemize}
+\item cos(x$^2$)-log(x)=0
+\item Does the equation have a root between 1,2.
+\end{itemize}
+
+\end{itemize}
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Solution 4}
+\label{sec-9}
+
+\lstset{language=Python}
+\begin{lstlisting}
+var('x')
+f(x)= x^5*log(x^7) 
+diff(f(x),x,5)
+
+var('x')
+integral(x*sin(x^2),x) 
+
+var('x')
+f=cos(x^2)-log(x)
+find_root(f(x)==0,1,2)
+\end{lstlisting}
+\end{frame}
+\begin{frame}
+\frametitle{Question 5}
+\label{sec-10}
+
+\begin{itemize}
+\item Find the determinant and inverse of :
+
+      A=[[x,0,1][y,1,0][z,0,y]]
+\end{itemize}
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Solution 5}
+\label{sec-11}
+
+\lstset{language=Python}
+\begin{lstlisting}
+var('x,y,z')
+A=matrix([[x,0,1],[y,1,0],[z,0,y]])
+A.det()
+A.inverse()
+\end{lstlisting}
+\end{frame}
+\begin{frame}
+\frametitle{Summary}
+\label{sec-12}
+
+\begin{itemize}
+\item We learnt about defining symbolic expression and functions.
+\item Using built-in constants and functions.
+\item Using <Tab> to see the documentation of a function.
+\item Simple calculus operations .
+\item Substituting values in expression using substitute function.
+\item Creating symbolic matrices and performing operation on them .
+\end{itemize}
+\end{frame}
+\begin{frame}
+\frametitle{Thank you!}
+\label{sec-13}
+
+  \begin{block}{}
+  \begin{center}
+  This spoken tutorial has been produced by the
+  \textcolor{blue}{FOSSEE} team, which is funded by the 
+  \end{center}
+  \begin{center}
+    \textcolor{blue}{National Mission on Education through \\
+      Information \& Communication Technology \\ 
+      MHRD, Govt. of India}.
+  \end{center}  
+  \end{block}
+\end{frame}
+
+\end{document}