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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: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> |
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5 % Copyright (c) 2005-2009, Prabhu Ramachandran |
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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{infolines} |
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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 |
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27 % Taken from Fernando's slides. |
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28 \usepackage{ae,aecompl} |
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29 \usepackage{mathpazo,courier,euler} |
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30 \usepackage[scaled=.95]{helvet} |
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31 |
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32 \definecolor{darkgreen}{rgb}{0,0.5,0} |
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33 |
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34 \usepackage{listings} |
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35 \lstset{language=Python, |
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36 basicstyle=\ttfamily\bfseries, |
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37 commentstyle=\color{red}\itshape, |
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38 stringstyle=\color{darkgreen}, |
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39 showstringspaces=false, |
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40 keywordstyle=\color{blue}\bfseries} |
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41 |
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42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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43 % Macros |
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44 \setbeamercolor{emphbar}{bg=blue!20, fg=black} |
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45 \newcommand{\emphbar}[1] |
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46 {\begin{beamercolorbox}[rounded=true]{emphbar} |
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47 {#1} |
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48 \end{beamercolorbox} |
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49 } |
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50 \newcounter{time} |
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51 \setcounter{time}{0} |
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52 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} |
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53 |
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54 \newcommand{\typ}[1]{\texttt{#1}} |
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55 |
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56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } |
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57 |
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58 %%% This is from Fernando's setup. |
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59 % \usepackage{color} |
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60 % \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} |
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61 % % Use and configure listings package for nicely formatted code |
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62 % \usepackage{listings} |
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63 % \lstset{ |
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64 % language=Python, |
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65 % basicstyle=\small\ttfamily, |
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66 % commentstyle=\ttfamily\color{blue}, |
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67 % stringstyle=\ttfamily\color{orange}, |
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68 % showstringspaces=false, |
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69 % breaklines=true, |
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70 % postbreak = \space\dots |
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71 % } |
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72 |
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73 |
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74 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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75 % Title page |
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76 \title[Exercises]{Exercises} |
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77 |
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78 \author[FOSSEE] {FOSSEE} |
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79 |
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80 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
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81 \date[] {8 November, 2009\\Day 2} |
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82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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83 |
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84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} |
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85 %\logo{\pgfuseimage{iitmlogo}} |
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86 |
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87 |
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88 %% Delete this, if you do not want the table of contents to pop up at |
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89 %% the beginning of each subsection: |
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90 \AtBeginSubsection[] |
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91 { |
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92 \begin{frame}<beamer> |
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93 \frametitle{Outline} |
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94 \tableofcontents[currentsection,currentsubsection] |
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95 \end{frame} |
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96 } |
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97 |
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98 |
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99 % If you wish to uncover everything in a step-wise fashion, uncomment |
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100 % the following command: |
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101 %\beamerdefaultoverlayspecification{<+->} |
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102 |
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103 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6} |
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104 |
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105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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106 % DOCUMENT STARTS |
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107 \begin{document} |
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108 |
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109 \begin{frame} |
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110 \titlepage |
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111 \end{frame} |
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112 |
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113 \begin{frame}{Problem 1.1} |
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114 The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example:\\ |
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115 aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\ |
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116 Write a function that returns the aliquot number of a given number. |
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117 \end{frame} |
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118 |
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119 \begin{frame}{Problem 1.2} |
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120 Pair of numbers (a, b) is said to be \alert{amicable} if aliquot number of a is b and aliquot number of b is a.\\ |
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121 Example: \texttt{220, 284}\\ |
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122 Write a program that prints all four digit amicable pairs. |
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123 |
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124 \inctime{20} |
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125 \end{frame} |
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126 |
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127 %% \begin{frame}{Problem 2} |
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128 %% Given an empty chessboard and one Bishop placed in any s%quare, say (r, c), generate the list of all squares the Bi%shop could move to. |
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129 |
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130 %% \end{frame} |
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131 |
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132 \begin{frame}[fragile] |
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133 \frametitle{Problem 2} |
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134 Given a string of numbers like, ``1, 3-7, 12, 15, 18-21'', produce the following list \\ |
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135 \begin{lstlisting} |
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136 [1,3,4,5,6,7,12,15,18,19,20,21] |
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137 \end{lstlisting} |
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138 \inctime{10} |
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139 \end{frame} |
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140 |
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141 \begin{frame} |
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142 \frametitle{Problem 3} |
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143 Count frequencies of words in a file. |
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144 \inctime{25} |
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145 \end{frame} |
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146 |
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147 \begin{frame}[fragile] |
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148 \frametitle{Problem set 4} |
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149 Central difference |
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150 \begin{equation*} |
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151 \frac{sin(x+h)-sin(x-h)}{2h} |
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152 \end{equation*} |
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153 \begin{lstlisting} |
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154 In []: x = linspace(0, 2*pi, 100) |
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155 In []: y = sin(x) |
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156 In []: deltax = x[1] - x[0] |
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157 \end{lstlisting} |
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158 \pause |
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159 \begin{enumerate} |
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160 \item Given this, get the finite difference of sin in the range 0 to 2*pi |
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161 \end{enumerate} |
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162 \end{frame} |
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163 |
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164 \begin{frame} |
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165 \frametitle{Problem Set 5} |
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166 \begin{itemize} |
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167 \item[5.1] Write a function that plots any regular n-gon given \typ{n}. |
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168 \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for |
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169 $k=2.5, 3.5$ and $4$ in the same plot. |
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170 \end{itemize} |
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171 \end{frame} |
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172 |
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173 \begin{frame}[fragile] |
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174 \frametitle{Problem Set 5} |
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175 \begin{columns} |
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176 \column{0.6\textwidth} |
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177 \small{ |
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178 \begin{itemize} |
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179 \item[3] Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$. Plot the successive iterates of this process as explained below. |
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180 \end{itemize}} |
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181 \column{0.35\textwidth} |
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182 \hspace*{-0.5in} |
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183 \includegraphics[height=1.6in, interpolate=true]{data/cobweb} |
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184 \end{columns} |
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185 \end{frame} |
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186 |
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187 \begin{frame} |
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188 \frametitle{Problem Set 5.3} |
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189 Plot the cobweb plot as follows: |
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190 \begin{enumerate} |
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191 \item Start at $(x_0, 0)$ ($\implies$ i=0) |
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192 \item Draw a line to $(x_i, f(x_i))$ |
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193 \item Set $x_{i+1} = f(x_i)$ |
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194 \item Draw a line to $(x_{i+1}, x_{i+1})$ |
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195 \item $(i\implies i+1)$ |
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196 \item Repeat from 2 for as long as you want |
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197 \end{enumerate} |
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198 \inctime{20} |
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199 \end{frame} |
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200 |
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201 \end{document} |