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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}