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diff --git a/getting_started_with_symbolics/slides.tex b/getting_started_with_symbolics/slides.tex index 51e8997..3f6552f 100644 --- a/getting_started_with_symbolics/slides.tex +++ b/getting_started_with_symbolics/slides.tex @@ -1,4 +1,4 @@ -% Created 2010-11-11 Thu 02:03 +% Created 2011-06-14 Tue 13:44 \documentclass[presentation]{beamer} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} @@ -23,14 +23,14 @@ commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, showstringspaces=false, keywordstyle=\color{blue}\bfseries} \providecommand{\alert}[1]{\textbf{#1}} -\title{Getting started with symbolics} +\title{} \author{FOSSEE} \date{} \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} \begin{document} -\maketitle + @@ -41,38 +41,66 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \begin{frame} -\frametitle{Outline} -\label{sec-1} + +\begin{center} +\vspace{12pt} +\textcolor{blue}{\huge Getting started with Symbolics} +\end{center} +\vspace{18pt} +\begin{center} +\vspace{10pt} +\includegraphics[scale=0.95]{../images/fossee-logo.png}\\ +\vspace{5pt} +\scriptsize Developed by FOSSEE Team, IIT-Bombay. \\ +\scriptsize Funded by National Mission on Education through ICT\\ +\scriptsize MHRD,Govt. of India\\ +\includegraphics[scale=0.30]{../images/iitb-logo.png}\\ +\end{center} +\end{frame} +\begin{frame} +\frametitle{Objectives} +\label{sec-2} + + At the end of this tutorial, you will be able to, + \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. +\item Define symbolic expressions in sage. +\item Use built-in constants and functions. +\item Perform Integration, differentiation using sage. +\item Define matrices. +\item Define Symbolic functions. +\item Simplify and solve symbolic expressions and functions. \end{itemize} \end{frame} \begin{frame} -\frametitle{Question 1} -\label{sec-2} +\frametitle{Pre-requisite} +\label{sec-3} + + Spoken tutorial on - + +\begin{itemize} +\item Getting started with Sage Notebook. +\end{itemize} +\end{frame} +\begin{frame} +\frametitle{Exercise 1} +\label{sec-4} + \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} +\label{sec-5} \lstset{language=Python} \begin{lstlisting} @@ -84,33 +112,29 @@ y^2-4*a*x \end{lstlisting} \end{frame} \begin{frame} -\frametitle{Question 2} -\label{sec-4} +\frametitle{Exercise 2} +\label{sec-6} \begin{itemize} \item Find the values of the following constants upto 6 digits precision - \begin{itemize} \item pi$^2$ -\item euler$_{\mathrm{gamma}}$$^2$ +\item euler\_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} +\label{sec-7} \lstset{language=Python} \begin{lstlisting} @@ -120,21 +144,23 @@ n(log(23,e)) \end{lstlisting} \end{frame} \begin{frame} -\frametitle{Question 3} -\label{sec-6} +\frametitle{Exercise 3} +\label{sec-8} + \begin{itemize} -\item Define the piecewise function. +\item Define the piecewise function\\ f(x)=3x+2 - when x is in the closed interval 0 to 4. + when x is in the closed interval 0 to 4\\ f(x)=4x$^2$ between 4 to 6. +\vspace{4pt} \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} +\label{sec-9} \lstset{language=Python} \begin{lstlisting} @@ -153,35 +179,32 @@ sum(f(n), n, 1, oo) \end{lstlisting} \end{frame} \begin{frame} -\frametitle{Question 4} -\label{sec-8} +\frametitle{Exercise 4} +\label{sec-10} + \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} - +\vspace{4pt} \item Integrate the given expression - \begin{itemize} \item x*sin(x$^2$) \end{itemize} - +\vspace{4pt} \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} +\label{sec-11} \lstset{language=Python} \begin{lstlisting} @@ -198,18 +221,19 @@ find_root(f(x)==0,1,2) \end{lstlisting} \end{frame} \begin{frame} -\frametitle{Question 5} -\label{sec-10} +\frametitle{Exercise 5} +\label{sec-12} + \begin{itemize} -\item Find the determinant and inverse of : +\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} +\label{sec-13} \lstset{language=Python} \begin{lstlisting} @@ -221,32 +245,71 @@ A.inverse() \end{frame} \begin{frame} \frametitle{Summary} -\label{sec-12} +\label{sec-14} +In this tutorial, we have learnt to, + + +\begin{itemize} +\item Define symbolic expression and functions using the method ``var``. +\item Use built-in constants like pi,e,oo and functions like + sum,sin,cos,log,exp and many more. +\item Use <Tab> to see the documentation of a function. +\item Do simple calculus using functions like -- +\begin{itemize} +\item diff()--to find a differential of a function +\item integral()--to integrate an expression +\item simplify--to simplify complicated expression. +\end{itemize} +\item Substitute values in expressions using ``substitute`` function. +\item Create symbolic matrices and perform operations on them like -- \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 . +\item det()--to find out the determinant of a matrix +\item inverse()--to find out the inverse of a matrix. +\end{itemize} \end{itemize} \end{frame} \begin{frame} -\frametitle{Thank you!} -\label{sec-13} +\frametitle{Evaluation} +\label{sec-15} + + +\begin{enumerate} +\item How do you define a name `y' as a symbol? +\vspace{8pt} +\item Get the value of pi upto precision 5 digits using sage? +\vspace{8pt} +\item Find third order differential function of + + f(x)=sin(x$^2$)+exp(x$^3$) +\end{enumerate} +\end{frame} +\begin{frame} +\frametitle{Solutions} +\label{sec-16} + + +\begin{enumerate} +\item var(`y') +\vspace{8pt} +\item n(pi,5) +\vspace{8pt} +\item diff(f(x),x,3) +\end{enumerate} +\end{frame} +\begin{frame} \begin{block}{} \begin{center} - This spoken tutorial has been produced by the - \textcolor{blue}{FOSSEE} team, which is funded by the + \textcolor{blue}{\Large THANK YOU!} \end{center} + \end{block} +\begin{block}{} \begin{center} - \textcolor{blue}{National Mission on Education through \\ - Information \& Communication Technology \\ - MHRD, Govt. of India}. + For more Information, visit our website\\ + \url{http://fossee.in/} \end{center} \end{block} \end{frame} -\end{document} +\end{document}
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