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    13 

    18 \tolerance=1000

    14 

    19 \usepackage[english]{babel} \usepackage{ae,aecompl}

    15 \title{Plotting Data }

    20 \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet}

    21 \usepackage{listings}

    22 \lstset{language=Python, basicstyle=\ttfamily\bfseries,

    23 commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen},

    24 showstringspaces=false, keywordstyle=\color{blue}\bfseries}

    25 \providecommand{\alert}[1]{\textbf{#1}}

    26 

    27 \title{Getting started with symbolics}

    17 \date{2010-09-14 Tue}

    29 \date{}

    18 

    30 

    31 \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent}

    28 \begin{frame}

    41 

    29 \frametitle{Tutorial Plan}

    42 

    43 

    44 \begin{frame}

    45 \frametitle{Outline}

    31 \begin{itemize}

    47 

    32 

    48 \begin{itemize}

    33 \item Defining symbolic expressions in sage.\\

    49 \item Defining symbolic expressions in sage.

    34 \label{sec-1.1}%

    50 \item Using built-in constants and functions.

    35 \item Using built-in costants and functions.\\

    51 \item Performing Integration, differentiation using sage.

    36 \label{sec-1.2}%

    52 \item Defining matrices.

    37 \item Performing Integration, differentiation using sage.\\

    53 \item Defining Symbolic functions.

    38 \label{sec-1.3}%

    54 \item Simplifying and solving symbolic expressions and functions.

    39 \item Defining matrices.\\

    55 \end{itemize}

    40 \label{sec-1.4}%

    56 \end{frame}

    41 \item Defining Symbolic functions.\\

    57 \begin{frame}

    42 \label{sec-1.5}%

    58 \frametitle{Questions 1}

    43 \item Simplifying and solving symbolic expressions and functions.\\

    59 \label{sec-2}

    44 \label{sec-1.6}%

    60 

    45 \end{itemize} % ends low level

    61 \begin{itemize}

    62 \item Define the following expression as symbolic

    63     expression in sage.

    64 

    65 \begin{itemize}

    66 \item x$^2$+y$^2$

    67 \item y$^2$-4ax

    68 \end{itemize}

    69 

    70 \end{itemize}

    71 

    72   

    73 \end{frame}

    74 \begin{frame}[fragile]

    75 \frametitle{Solutions 1}

    76 \label{sec-3}

    77 

    78 \begin{verbatim}

    79 var('x,y')

    80 x^2+y^2

    81 

    82 var('a,x,y')

    83 y^2-4*a*x

    84 \end{verbatim}

    85 \end{frame}

    86 \begin{frame}

    87 \frametitle{Questions 2}

    88 \label{sec-4}

    89 

    90 \begin{itemize}

    91 \item Find the values of the following constants upto 6 digits  precision

    92 

    93 \begin{itemize}

    94 \item pi$^2$

    95 \end{itemize}

    96 

    97 \item Find the value of the following.

    98 

    99 \begin{itemize}

   100 \item sin(pi/4)

   101 \item ln(23)

   102 \end{itemize}

   103 

   104 \end{itemize}

   105 \end{frame}

   106 \begin{frame}[fragile]

   107 \frametitle{Solutions 2}

   108 \label{sec-5}

   109 

   110 \begin{verbatim}

   111 n(pi^2,digits=6)

   112 n(sin(pi/4))

   113 n(log(23,e))

   114 \end{verbatim}

   115 \end{frame}

   116 \begin{frame}

   117 \frametitle{Question 2}

   118 \label{sec-6}

   119 

   120 \begin{itemize}

   121 \item Define the piecewise function. 

   122    f(x)=3x+2 

   123    when x is in the closed interval 0 to 4.

   124    f(x)=4x$^2$

   125    between 4 to 6.

   126 \item Sum  of 1/(n$^2$-1) where n ranges from 1 to infinity.

   127 \end{itemize}

   128 \end{frame}

   129 \begin{frame}[fragile]

   130 \frametitle{Solution Q1}

   131 \label{sec-7}

   132 

   133 \begin{verbatim}

   134 var('x') 

   135 h(x)=3*x+2 

   136 g(x)= 4*x^2

   137 f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x)

   138 f

   139 \end{verbatim}

   140 \end{frame}

   141 \begin{frame}[fragile]

   142 \frametitle{Solution Q2}

   143 \label{sec-8}

   144 

   145 \begin{verbatim}

   146 var('n')

   147 f=1/(n^2-1) 

   148 sum(f(n), n, 1, oo)

   149 \end{verbatim}

   150  

   151 \end{frame}

   152 \begin{frame}

   153 \frametitle{Questions 3}

   154 \label{sec-9}

   155 

   156 \begin{itemize}

   157 \item Differentiate the following.

   158 

   159 \begin{itemize}

   160 \item x$^5$*log(x$^7$)  , degree=4

   161 \end{itemize}

   162 

   163 \item Integrate the given expression

   164 

   165 \begin{itemize}

   166 \item x*sin(x$^2$)

   167 \end{itemize}

   168 

   169 \item Find x

   170 

   171 \begin{itemize}

   172 \item cos(x$^2$)-log(x)=0

   173 \item Does the equation have a root between 1,2.

   174 \end{itemize}

   175 

   176 \end{itemize}

   177 \end{frame}

   178 \begin{frame}[fragile]

   179 \frametitle{Solutions 3}

   180 \label{sec-10}

   181 

   182 \begin{verbatim}

   183 var('x')

   184 f(x)= x^5*log(x^7) 

   185 diff(f(x),x,5)

   186 

   187 var('x')

   188 integral(x*sin(x^2),x) 

   189 

   190 var('x')

   191 f=cos(x^2)-log(x)

   192 find_root(f(x)==0,1,2)

   193 \end{verbatim}

   194 \end{frame}

   195 \begin{frame}

   196 \frametitle{Question 4}

   197 \label{sec-11}

   198 

   199 \begin{itemize}

   200 \item Find the determinant and inverse of :

   201 

   202       A=[[x,0,1][y,1,0][z,0,y]]

   203 \end{itemize}

   204 \end{frame}

   205 \begin{frame}[fragile]

   206 \frametitle{Solution 4}

   207 \label{sec-12}

   208 

   209 \begin{verbatim}

   210 var('x,y,z')

   211 A=matrix([[x,0,1],[y,1,0],[z,0,y]])

   212 A.det()

   213 A.inverse()

   214 \end{verbatim}

    49 \label{sec-2}

   218 \label{sec-13}

    50 \begin{itemize}

   219 

    51 

   220 \begin{itemize}

    52 \item We learnt about defining symbolic expression and functions.\\

   221 \item We learnt about defining symbolic 

    53 \label{sec-2.1}%

   222    expression and functions.

    54 \item Using built-in constants and functions.\\

   223 \item Using built-in constants and functions.

    55 \label{sec-2.2}%

   224 \item Using <Tab>  to see the documentation of a 

    56 \item Using <Tab>  to see the documentation of a function.\\

   225    function.

    57 \label{sec-2.3}%

   226 \end{itemize}

    58 \item Simple calculus operations .\\

   227 

    59 \label{sec-2.4}%

   228  

    60 \item Substituting values in expression using substitute function.\\

   229 \end{frame}

    61 \label{sec-2.5}%

   230 \begin{frame}

    62 \item Creating symbolic matrices and performing operation on them .\\

   231 \frametitle{Summary}

    63 \label{sec-2.6}%

   232 \label{sec-14}

    64 \end{itemize} % ends low level

   233 

   234 \begin{itemize}

   235 \item Simple calculus operations .

   236 \item Substituting values in expression 

   237    using substitute function.

   238 \item Creating symbolic matrices and 

   239    performing operation on them .

   240 \end{itemize}

   241 \end{frame}

   242 \begin{frame}

   243 \frametitle{Thank you!}

   244 \label{sec-15}

   245 

   246   \begin{block}{}

   247   \begin{center}

   248   This spoken tutorial has been produced by the

   249   \textcolor{blue}{FOSSEE} team, which is funded by the 

   250   \end{center}

   251   \begin{center}

   252     \textcolor{blue}{National Mission on Education through \\

   253       Information \& Communication Technology \\ 

   254       MHRD, Govt. of India}.

   255   \end{center}  

   256   \end{block}