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1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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2 %Tutorial slides on Python. |
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3 % |
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4 % Author: FOSSEE |
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5 % Copyright (c) 2009, FOSSEE, IIT Bombay |
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6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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7 |
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8 \documentclass[14pt,compress]{beamer} |
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9 %\documentclass[draft]{beamer} |
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10 %\documentclass[compress,handout]{beamer} |
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11 %\usepackage{pgfpages} |
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12 %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] |
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13 |
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14 % Modified from: generic-ornate-15min-45min.de.tex |
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15 \mode<presentation> |
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16 { |
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17 \usetheme{Warsaw} |
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18 \useoutertheme{split} |
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19 \setbeamercovered{transparent} |
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20 } |
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21 |
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22 \usepackage[english]{babel} |
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23 \usepackage[latin1]{inputenc} |
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24 %\usepackage{times} |
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25 \usepackage[T1]{fontenc} |
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26 \usepackage{amsmath} |
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27 |
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28 % Taken from Fernando's slides. |
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29 \usepackage{ae,aecompl} |
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30 \usepackage{mathpazo,courier,euler} |
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31 \usepackage[scaled=.95]{helvet} |
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32 |
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33 \definecolor{darkgreen}{rgb}{0,0.5,0} |
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34 |
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35 \usepackage{listings} |
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36 \lstset{language=Python, |
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37 basicstyle=\ttfamily\bfseries, |
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38 commentstyle=\color{red}\itshape, |
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39 stringstyle=\color{darkgreen}, |
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40 showstringspaces=false, |
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41 keywordstyle=\color{blue}\bfseries} |
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42 |
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43 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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44 % Macros |
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45 \setbeamercolor{emphbar}{bg=blue!20, fg=black} |
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46 \newcommand{\emphbar}[1] |
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47 {\begin{beamercolorbox}[rounded=true]{emphbar} |
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48 {#1} |
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49 \end{beamercolorbox} |
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50 } |
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51 \newcounter{time} |
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52 \setcounter{time}{0} |
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53 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} |
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54 |
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55 \newcommand{\typ}[1]{\lstinline{#1}} |
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56 |
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57 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } |
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58 |
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59 %%% This is from Fernando's setup. |
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60 % \usepackage{color} |
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61 % \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} |
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62 % % Use and configure listings package for nicely formatted code |
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63 % \usepackage{listings} |
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64 % \lstset{ |
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65 % language=Python, |
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66 % basicstyle=\small\ttfamily, |
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67 % commentstyle=\ttfamily\color{blue}, |
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68 % stringstyle=\ttfamily\color{orange}, |
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69 % showstringspaces=false, |
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70 % breaklines=true, |
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71 % postbreak = \space\dots |
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72 % } |
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73 |
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74 |
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75 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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76 % Title page |
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77 \title[Basic Python]{Interpolation, Differentiation and Integration} |
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78 |
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79 \author[FOSSEE] {FOSSEE} |
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80 |
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81 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
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82 \date[] {31, October 2009\\Day 1, Session 4} |
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83 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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84 |
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85 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} |
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86 %\logo{\pgfuseimage{iitmlogo}} |
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87 |
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88 |
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89 %% Delete this, if you do not want the table of contents to pop up at |
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90 %% the beginning of each subsection: |
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91 \AtBeginSubsection[] |
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92 { |
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93 \begin{frame}<beamer> |
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94 \frametitle{Outline} |
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95 \tableofcontents[currentsection,currentsubsection] |
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96 \end{frame} |
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97 } |
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98 |
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99 %%\AtBeginSection[] |
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100 %%{ |
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101 %%\begin{frame}<beamer> |
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102 %% \frametitle{Outline} |
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103 %% \tableofcontents[currentsection,currentsubsection] |
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104 %%\end{frame} |
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105 %%} |
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106 |
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107 % If you wish to uncover everything in a step-wise fashion, uncomment |
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108 % the following command: |
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109 %\beamerdefaultoverlayspecification{<+->} |
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110 |
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111 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6} |
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112 |
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113 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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114 % DOCUMENT STARTS |
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115 \begin{document} |
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116 |
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117 \begin{frame} |
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118 \titlepage |
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119 \end{frame} |
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120 |
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121 \begin{frame} |
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122 \frametitle{Outline} |
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123 \tableofcontents |
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124 % \pausesections |
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125 \end{frame} |
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126 |
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127 \section{Integration} |
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128 |
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129 \subsection{Quadrature} |
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130 |
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131 \begin{frame}[fragile] |
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132 \frametitle{Quadrature} |
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133 \begin{itemize} |
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134 \item We wish to find area under a curve |
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135 \item Area under $(sin(x) + x^2)$ in $(0,1)$ |
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136 \item scipy has functions to do that |
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137 \end{itemize} |
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138 \small{\typ{In []: from scipy.integrate import quad}} |
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139 \begin{itemize} |
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140 \item Inputs - function to integrate, limits |
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141 \end{itemize} |
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142 \begin{lstlisting} |
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143 In []: x = 0 |
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144 In []: quad(sin(x)+x**2, 0, 1) |
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145 \end{lstlisting} |
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146 \alert{\typ{error:}} |
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147 \typ{First argument must be a callable function.} |
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148 \end{frame} |
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149 |
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150 \begin{frame}[fragile] |
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151 \frametitle{Functions - Definition} |
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152 \begin{lstlisting} |
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153 In []: def f(x): |
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154 return sin(x)+x**2 |
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155 In []: quad(f, 0, 1) |
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156 \end{lstlisting} |
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157 \begin{itemize} |
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158 \item \typ{def} |
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159 \item arguments |
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160 \item \typ{return} |
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161 \end{itemize} |
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162 \end{frame} |
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163 |
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164 \begin{frame}[fragile] |
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165 \frametitle{Functions - Calling them} |
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166 \begin{lstlisting} |
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167 In [15]: f() |
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168 --------------------------------------- |
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169 \end{lstlisting} |
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170 \alert{\typ{TypeError:}}\typ{f() takes exactly 1 argument} |
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171 \typ{(0 given)} |
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172 \begin{lstlisting} |
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173 In []: f(0) |
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174 Out[]: 0.0 |
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175 In []: f(1) |
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176 Out[]: 1.8414709848078965 |
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177 \end{lstlisting} |
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178 \end{frame} |
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179 |
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180 |
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181 \begin{frame}[fragile] |
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182 \frametitle{Functions - Default Arguments} |
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183 \begin{lstlisting} |
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184 In []: def f(x=1): |
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185 return sin(x)+x**2 |
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186 In []: f(10) |
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187 Out[]: 99.455978889110625 |
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188 In []: f(1) |
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189 Out[]: 1.8414709848078965 |
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190 In []: f() |
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191 Out[]: 1.8414709848078965 |
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192 \end{lstlisting} |
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193 \end{frame} |
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194 |
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195 \begin{frame}[fragile] |
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196 \frametitle{Functions - Keyword Arguments} |
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197 \begin{lstlisting} |
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198 In []: def f(x=1, y=pi): |
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199 return sin(y)+x**2 |
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200 In []: f() |
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201 Out[]: 1.0000000000000002 |
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202 In []: f(2) |
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203 Out[]: 4.0 |
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204 In []: f(y=2) |
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205 Out[]: 1.9092974268256817 |
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206 In []: f(y=pi/2,x=0) |
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207 Out[]: 1.0 |
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208 \end{lstlisting} |
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209 \end{frame} |
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210 |
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211 \begin{frame}[fragile] |
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212 \frametitle{More on functions} |
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213 \begin{itemize} |
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214 \item Scope of variables in the function is local |
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215 \item Mutable items are \alert{passed by reference} |
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216 \item First line after definition may be a documentation string |
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217 (\alert{recommended!}) |
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218 \item Function definition and execution defines a name bound to the |
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219 function |
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220 \item You \emph{can} assign a variable to a function! |
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221 \end{itemize} |
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222 \end{frame} |
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223 |
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224 \begin{frame}[fragile] |
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225 \frametitle{Quadrature \ldots} |
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226 \begin{lstlisting} |
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227 In []: quad(f, 0, 1) |
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228 \end{lstlisting} |
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229 Returns the integral and an estimate of the absolute error in the result. |
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230 \begin{itemize} |
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231 \item Use \typ{dblquad} for Double integrals |
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232 \item Use \typ{tplquad} for Triple integrals |
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233 \end{itemize} |
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234 \end{frame} |
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235 |
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236 \subsection{ODEs} |
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237 |
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238 \begin{frame}[fragile] |
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239 \frametitle{ODE Integration} |
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240 We shall use the simple ODE of a simple pendulum. |
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241 \begin{equation*} |
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242 \ddot{\theta} = -\frac{g}{L}sin(\theta) |
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243 \end{equation*} |
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244 \begin{itemize} |
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245 \item This equation can be written as a system of two first order ODEs |
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246 \end{itemize} |
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247 \begin{align} |
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248 \dot{\theta} &= \omega \\ |
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249 \dot{\omega} &= -\frac{g}{L}sin(\theta) \\ |
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250 \text{At}\ t &= 0 : \nonumber \\ |
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251 \theta = \theta_0\quad & \&\quad \omega = 0 \nonumber |
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252 \end{align} |
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253 \end{frame} |
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254 |
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255 \begin{frame}[fragile] |
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256 \frametitle{Solving ODEs using SciPy} |
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257 \begin{itemize} |
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258 \item We use the \typ{odeint} function from scipy to do the integration |
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259 \item Define a function as below |
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260 \end{itemize} |
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261 \begin{lstlisting} |
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262 In []: def pend_int(unknown, t, p): |
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263 .... theta, omega = unknown |
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264 .... g, L = p |
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265 .... f=[omega, -(g/L)*sin(theta)] |
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266 .... return f |
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267 .... |
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268 \end{lstlisting} |
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269 \end{frame} |
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270 |
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271 \begin{frame}[fragile] |
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272 \frametitle{Solving ODEs using SciPy \ldots} |
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273 \begin{itemize} |
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274 \item \typ{t} is the time variable \\ |
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275 \item \typ{p} has the constants \\ |
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276 \item \typ{initial} has the initial values |
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277 \end{itemize} |
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278 \begin{lstlisting} |
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279 In []: t = linspace(0, 10, 101) |
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280 In []: p=(-9.81, 0.2) |
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281 In []: initial = [10*2*pi/360, 0] |
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282 \end{lstlisting} |
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283 \end{frame} |
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284 |
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285 \begin{frame}[fragile] |
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286 \frametitle{Solving ODEs using SciPy \ldots} |
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287 |
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288 \small{\typ{In []: from scipy.integrate import odeint}} |
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289 \begin{lstlisting} |
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290 In []: pend_sol = odeint(pend_int, |
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291 initial,t, |
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292 args=(p,)) |
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293 \end{lstlisting} |
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294 \end{frame} |
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295 |
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296 \begin{frame} |
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297 \frametitle{Things we have learned} |
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298 \begin{itemize} |
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299 \item Functions |
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300 \begin{itemize} |
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301 \item Definition |
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302 \item Calling |
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303 \item Default Arguments |
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304 \item Keyword Arguments |
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305 \end{itemize} |
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306 \item Quadrature |
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307 \end{itemize} |
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308 \end{frame} |
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309 |
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310 \end{document} |
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311 |