author | Puneeth Chaganti <punchagan@fossee.in> |
Wed, 04 Nov 2009 10:35:53 +0530 | |
changeset 267 | 978d06520462 |
parent 263 | 8a4a1e5aec85 |
child 288 | c4e25269a86c |
permissions | -rw-r--r-- |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%Tutorial slides on Python. |
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% |
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% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> |
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% Copyright (c) 2005-2009, Prabhu Ramachandran |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\documentclass[14pt,compress]{beamer} |
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%\documentclass[draft]{beamer} |
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%\documentclass[compress,handout]{beamer} |
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%\usepackage{pgfpages} |
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%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] |
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% Modified from: generic-ornate-15min-45min.de.tex |
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\mode<presentation> |
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{ |
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\usetheme{Warsaw} |
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\useoutertheme{infolines} |
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\setbeamercovered{transparent} |
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} |
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\usepackage[english]{babel} |
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\usepackage[latin1]{inputenc} |
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%\usepackage{times} |
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\usepackage[T1]{fontenc} |
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% Taken from Fernando's slides. |
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\usepackage{ae,aecompl} |
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\usepackage{mathpazo,courier,euler} |
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\usepackage[scaled=.95]{helvet} |
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\definecolor{darkgreen}{rgb}{0,0.5,0} |
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\usepackage{listings} |
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\lstset{language=Python, |
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basicstyle=\ttfamily\bfseries, |
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commentstyle=\color{red}\itshape, |
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stringstyle=\color{darkgreen}, |
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showstringspaces=false, |
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keywordstyle=\color{blue}\bfseries} |
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Macros |
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\setbeamercolor{emphbar}{bg=blue!20, fg=black} |
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\newcommand{\emphbar}[1] |
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{\begin{beamercolorbox}[rounded=true]{emphbar} |
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{#1} |
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\end{beamercolorbox} |
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} |
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\newcounter{time} |
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\setcounter{time}{0} |
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} |
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\newcommand{\typ}[1]{\texttt{#1}} |
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\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } |
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%%% This is from Fernando's setup. |
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% \usepackage{color} |
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% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} |
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% % Use and configure listings package for nicely formatted code |
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% \usepackage{listings} |
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% \lstset{ |
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% language=Python, |
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% basicstyle=\small\ttfamily, |
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% commentstyle=\ttfamily\color{blue}, |
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% stringstyle=\ttfamily\color{orange}, |
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% showstringspaces=false, |
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% breaklines=true, |
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% postbreak = \space\dots |
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% } |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Title page |
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\title[Exercises]{Exercises} |
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\author[FOSSEE] {FOSSEE} |
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
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\date[] {1 November, 2009\\Day 2, Session 4} |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} |
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%\logo{\pgfuseimage{iitmlogo}} |
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%% Delete this, if you do not want the table of contents to pop up at |
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%% the beginning of each subsection: |
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\AtBeginSubsection[] |
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{ |
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\begin{frame}<beamer> |
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\frametitle{Outline} |
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\tableofcontents[currentsection,currentsubsection] |
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\end{frame} |
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} |
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% If you wish to uncover everything in a step-wise fashion, uncomment |
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% the following command: |
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%\beamerdefaultoverlayspecification{<+->} |
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%\includeonlyframes{current,current1,current2,current3,current4,current5,current6} |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% DOCUMENT STARTS |
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\begin{document} |
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\begin{frame} |
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\titlepage |
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\end{frame} |
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\begin{frame}{Problem 1.1} |
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The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. \\For example: |
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\center{aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.}\\ |
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Write a function that returns the aliquot number of a given number. |
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\end{frame} |
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\begin{frame}{Problem 1.2} |
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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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Example: \texttt{220, 284}\\ |
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Write a program that prints all four digit amicable pairs. |
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|
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\inctime{20} |
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\end{frame} |
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|
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%% \begin{frame}{Problem 2} |
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%% 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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|
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%% \end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Problem Set 2} |
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Given a string like, ``1, 3-7, 12, 15, 18-21'', produce the list \\ |
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\begin{lstlisting} |
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[1,3,4,5,6,7,12,15,18,19,20,21] |
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\end{lstlisting} |
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\inctime{10} |
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139 |
\end{frame} |
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|
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141 |
\begin{frame} |
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\frametitle{Problem Set 3} |
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\begin{description} |
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\item[3.1] Count word frequencies in a file. |
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\end{description} |
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\inctime{5} |
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\end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Problem set 4} |
219
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151 |
Central difference |
206
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\begin{equation*} |
219
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\frac{sin(x+h)-sin(x-h)}{2h} |
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\end{equation*} |
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\begin{lstlisting} |
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In []: x = linspace(0, 2*pi, 100) |
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In []: y = sin(x) |
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In []: deltax = x[1] - x[0] |
206
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159 |
\end{lstlisting} |
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\pause |
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\begin{enumerate} |
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\item Given this, get the finite difference of sin in the range 0 to 2*pi |
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163 |
\end{enumerate} |
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164 |
\end{frame} |
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|
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166 |
\begin{frame} |
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\frametitle{Problem Set 5} |
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\begin{itemize} |
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\item[5.1] Write a function that plots any regular n-gon given \typ{n}. |
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\item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for |
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$k=2.5, 3.5$ and $4$ in the same plot. |
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172 |
\end{itemize} |
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\end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Problem Set 5} |
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177 |
\begin{columns} |
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\column{0.6\textwidth} |
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\small{ |
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\begin{itemize} |
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\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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182 |
\end{itemize}} |
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\column{0.35\textwidth} |
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184 |
\hspace*{-0.5in} |
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\includegraphics[height=1.6in, interpolate=true]{data/cobweb} |
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186 |
\end{columns} |
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187 |
\end{frame} |
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188 |
|
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189 |
\begin{frame} |
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\frametitle{Problem Set 5.3} |
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191 |
Plot the cobweb plot as follows: |
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192 |
\begin{enumerate} |
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\item Start at $(x_0, 0)$ ($\implies$ i=0) |
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\item Draw a line to $(x_i, f(x_i))$ |
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\item Set $x_{i+1} = f(x_i)$ |
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\item Draw a line to $(x_{i+1}, x_{i+1})$ |
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197 |
\item $(i\implies i+1)$ |
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198 |
\item Repeat from 2 for as long as you want |
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199 |
\end{enumerate} |
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200 |
\inctime{20} |
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201 |
\end{frame} |
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202 |
|
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203 |
\end{document} |