author | Puneeth Chaganti <punchagan@fossee.in> |
Wed, 01 Dec 2010 16:51:35 +0530 | |
changeset 522 | d33698326409 |
permissions | -rw-r--r-- |
522
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1 |
% 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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|
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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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|
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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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|
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\end{itemize} |
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|
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\begin{itemize} |
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\item Find the value of the following. |
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|
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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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107 |
\end{itemize} |
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|
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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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113 |
\label{sec-5} |
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|
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\lstset{language=Python} |
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116 |
\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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120 |
\end{lstlisting} |
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121 |
\end{frame} |
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122 |
\begin{frame} |
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123 |
\frametitle{Question 3} |
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124 |
\label{sec-6} |
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125 |
|
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126 |
\begin{itemize} |
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127 |
\item Define the piecewise function. |
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128 |
f(x)=3x+2 |
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129 |
when x is in the closed interval 0 to 4. |
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f(x)=4x$^2$ |
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131 |
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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133 |
\end{itemize} |
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134 |
\end{frame} |
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135 |
\begin{frame}[fragile] |
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\frametitle{Solution 3} |
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137 |
\label{sec-7} |
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138 |
|
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139 |
\lstset{language=Python} |
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140 |
\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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145 |
f |
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146 |
\end{lstlisting} |
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147 |
|
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148 |
\lstset{language=Python} |
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149 |
\begin{lstlisting} |
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150 |
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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153 |
\end{lstlisting} |
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154 |
\end{frame} |
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155 |
\begin{frame} |
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156 |
\frametitle{Question 4} |
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157 |
\label{sec-8} |
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158 |
|
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159 |
\begin{itemize} |
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160 |
\item Differentiate the following. |
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161 |
|
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162 |
\begin{itemize} |
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163 |
\item sin(x$^3$)+log(3x), to the second order |
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164 |
\item x$^5$*log(x$^7$), to the fourth order |
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165 |
\end{itemize} |
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166 |
|
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167 |
\item Integrate the given expression |
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168 |
|
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169 |
\begin{itemize} |
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170 |
\item x*sin(x$^2$) |
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171 |
\end{itemize} |
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172 |
|
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173 |
\item Find x |
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174 |
|
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175 |
\begin{itemize} |
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176 |
\item cos(x$^2$)-log(x)=0 |
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177 |
\item Does the equation have a root between 1,2. |
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178 |
\end{itemize} |
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179 |
|
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180 |
\end{itemize} |
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181 |
\end{frame} |
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182 |
\begin{frame}[fragile] |
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183 |
\frametitle{Solution 4} |
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184 |
\label{sec-9} |
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185 |
|
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186 |
\lstset{language=Python} |
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187 |
\begin{lstlisting} |
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188 |
var('x') |
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189 |
f(x)= x^5*log(x^7) |
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190 |
diff(f(x),x,5) |
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191 |
|
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192 |
var('x') |
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193 |
integral(x*sin(x^2),x) |
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|
194 |
|
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195 |
var('x') |
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196 |
f=cos(x^2)-log(x) |
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197 |
find_root(f(x)==0,1,2) |
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198 |
\end{lstlisting} |
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199 |
\end{frame} |
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200 |
\begin{frame} |
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201 |
\frametitle{Question 5} |
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202 |
\label{sec-10} |
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203 |
|
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204 |
\begin{itemize} |
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205 |
\item Find the determinant and inverse of : |
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206 |
|
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207 |
A=[[x,0,1][y,1,0][z,0,y]] |
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208 |
\end{itemize} |
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209 |
\end{frame} |
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210 |
\begin{frame}[fragile] |
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211 |
\frametitle{Solution 5} |
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212 |
\label{sec-11} |
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213 |
|
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214 |
\lstset{language=Python} |
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215 |
\begin{lstlisting} |
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216 |
var('x,y,z') |
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217 |
A=matrix([[x,0,1],[y,1,0],[z,0,y]]) |
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218 |
A.det() |
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219 |
A.inverse() |
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220 |
\end{lstlisting} |
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221 |
\end{frame} |
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222 |
\begin{frame} |
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223 |
\frametitle{Summary} |
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224 |
\label{sec-12} |
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225 |
|
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226 |
\begin{itemize} |
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227 |
\item We learnt about defining symbolic expression and functions. |
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228 |
\item Using built-in constants and functions. |
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229 |
\item Using <Tab> to see the documentation of a function. |
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230 |
\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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|
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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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|
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\end{document} |