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