1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
2 %Tutorial slides on Python. |
2 %Tutorial slides on Python. |
3 % |
3 % |
4 % Author: FOSSEE |
4 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> |
5 % Copyright (c) 2009, FOSSEE, IIT Bombay |
5 % Copyright (c) 2005-2009, Prabhu Ramachandran |
6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
7 |
7 |
8 \documentclass[14pt,compress]{beamer} |
8 \documentclass[14pt,compress]{beamer} |
9 %\documentclass[draft]{beamer} |
9 %\documentclass[draft]{beamer} |
10 %\documentclass[compress,handout]{beamer} |
10 %\documentclass[compress,handout]{beamer} |
116 |
108 |
117 \begin{frame} |
109 \begin{frame} |
118 \titlepage |
110 \titlepage |
119 \end{frame} |
111 \end{frame} |
120 |
112 |
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113 |
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114 \begin{frame}[fragile] |
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115 \frametitle{Problem 1} |
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116 \begin{columns} |
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117 \column{0.5\textwidth} |
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118 \hspace*{-0.5in} |
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119 \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png} |
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120 \column{0.45\textwidth} |
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121 \begin{block}{Example code} |
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122 \tiny |
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123 \begin{lstlisting} |
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124 l = [] |
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125 t = [] |
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126 for line in open('pendulum.txt'): |
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127 point = line.split() |
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128 l.append(float(point[0])) |
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129 t.append(float(point[1])) |
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130 tsq = [] |
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131 for time in t: |
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132 tsq.append(time*time) |
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133 plot(l, tsq, '.') |
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134 \end{lstlisting} |
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135 \end{block} |
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136 \end{columns} |
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137 \begin{block}{Problem Statement} |
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138 Tweak above code to plot data in file 'location.txt'. |
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139 \end{block} |
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140 \end{frame} |
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141 |
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142 \begin{frame} |
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143 \frametitle{Problem 1 cont...} |
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144 \begin{itemize} |
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145 \item Label both the axes. |
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146 \item What kind of motion is this? |
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147 \item Title the graph accordingly. |
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148 \item Annotate the position where vertical velocity is zero. |
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149 \end{itemize} |
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150 \end{frame} |
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151 |
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152 \begin{frame}[fragile] |
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153 \frametitle{Problem 2} |
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154 \begin{columns} |
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155 \column{0.5\textwidth} |
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156 \hspace*{-0.5in} |
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157 \includegraphics[height=2in, interpolate=true]{data/points} |
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158 \column{0.45\textwidth} |
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159 \begin{block}{Line between two points} |
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160 \tiny |
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161 \begin{lstlisting} |
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162 In []: x = [1, 5] |
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163 In []: y = [1, 4] |
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164 In []: plot(x, y) |
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165 \end{lstlisting} |
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166 \end{block} |
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167 \end{columns} |
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168 Line can be plotted using arrays of coordinates. |
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169 \pause |
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170 \begin{block}{Problem statement} |
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171 Write a Program that plots a regular n-gon(Let n = 5). |
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172 \end{block} |
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173 \end{frame} |
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174 |
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175 |
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176 \begin{frame}[fragile] |
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177 \frametitle{Problem 3} |
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178 \begin{columns} |
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179 \column{0.5\textwidth} |
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180 \hspace*{-0.5in} |
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181 \includegraphics[height=2in, interpolate=true]{data/damp} |
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182 \column{0.45\textwidth} |
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183 \begin{block}{Damped Oscillation} |
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184 \tiny |
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185 \begin{lstlisting} |
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186 In []: x = linspace(0, 4*pi) |
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187 In []: plot(x, exp(x/10)*sin(x)) |
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188 \end{lstlisting} |
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189 \end{block} |
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190 \end{columns} |
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191 \end{frame} |
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192 |
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193 \begin{frame}[fragile] |
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194 \frametitle{Problem 3 cont...} |
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195 Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time. |
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196 \begin{columns} |
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197 \column{0.35\textwidth} |
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198 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2} |
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199 \column{0.35\textwidth} |
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200 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot4} |
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201 \column{0.35\textwidth} |
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202 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot6} |
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203 \end{columns} |
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204 \begin{block}{Hint} |
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205 \small |
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206 \begin{lstlisting} |
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207 savefig('plot'+str(i)+'.png') #i is int variable |
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208 \end{lstlisting} |
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209 \end{block} |
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210 \end{frame} |
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211 |
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212 \begin{frame}[fragile] |
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213 \frametitle{Problem 4} |
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214 \begin{lstlisting} |
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215 In []: x = imread('smoothing.png') |
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216 In []: x.shape |
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217 Out[]: (256, 256) |
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218 In []: imshow(x,cmap=cm.gray) |
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219 \end{lstlisting} |
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220 \emphbar{Replace each pixel with mean of neighboring pixels} |
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221 \begin{center} |
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222 \includegraphics[height=1in, interpolate=true]{data/neighbour} |
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223 \end{center} |
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224 \end{frame} |
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225 |
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226 \begin{frame} |
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227 \begin{center} |
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228 \includegraphics[height=3in, interpolate=true]{data/smoothing} |
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229 \end{center} |
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230 \end{frame} |
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231 |
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232 \begin{frame}[fragile] |
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233 \frametitle{Problem 4: Approach} |
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234 For \typ{y} being resultant image: |
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235 \begin{lstlisting} |
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236 y[1, 1] = x[0, 1]/4 + x[1, 0]/4 |
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237 + x[2, 1]/4 + x[1, 2]/4 |
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238 \end{lstlisting} |
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239 \begin{columns} |
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240 \column{0.45\textwidth} |
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241 \hspace*{-0.5in} |
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242 \includegraphics[height=1.5in, interpolate=true]{data/smoothing} |
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243 \column{0.45\textwidth} |
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244 \hspace*{-0.5in} |
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245 \includegraphics[height=1.5in, interpolate=true]{data/after-filter} |
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246 \end{columns} |
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247 \begin{block}{Hint:} |
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248 Use array Slicing. |
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249 \end{block} |
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250 \end{frame} |
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251 |
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252 \begin{frame}[fragile] |
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253 \frametitle{Solution} |
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254 \begin{lstlisting} |
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255 In []: y = zeros_like(x) |
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256 In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+ |
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257 x[2:,1:-1]/4+ |
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258 x[1:-1,2:]/4+ |
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259 x[1:-1,:-2]/4 |
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260 In []: imshow(y,cmap=cm.gray) |
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261 \end{lstlisting} |
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262 \end{frame} |
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263 |
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264 |
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265 \end{document} |
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266 |
121 %% \begin{frame} |
267 %% \begin{frame} |
122 %% \frametitle{Outline} |
268 %% \frametitle{Problem 4} |
123 %% \tableofcontents |
269 %% Legendre polynomials $P_n(x)$ are defined by the following recurrence relation |
124 %% % \pausesections |
270 |
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271 %% \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\ |
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272 |
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273 %% with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three |
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274 %% Legendre polynomials and plot all 6 over the interval [-1,1]. |
125 %% \end{frame} |
275 %% \end{frame} |
126 |
276 |
127 |
277 %% \begin{frame}[fragile] |
128 \end{document} |
278 %% \frametitle{Problem Set 5} |
129 |
279 %% \begin{columns} |
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280 %% \column{0.6\textwidth} |
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281 %% \small{ |
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282 %% \begin{itemize} |
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283 %% \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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284 %% \end{itemize}} |
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285 %% \column{0.35\textwidth} |
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286 %% \hspace*{-0.5in} |
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287 %% \includegraphics[height=1.6in, interpolate=true]{data/cobweb} |
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288 %% \end{columns} |
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289 %% \end{frame} |
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290 |
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291 %% \begin{frame} |
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292 %% \frametitle{Problem Set 5.3} |
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293 %% Plot the cobweb plot as follows: |
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294 %% \begin{enumerate} |
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295 %% \item Start at $(x_0, 0)$ ($\implies$ i=0) |
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296 %% \item Draw a line to $(x_i, f(x_i))$ |
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297 %% \item Set $x_{i+1} = f(x_i)$ |
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298 %% \item Draw a line to $(x_{i+1}, x_{i+1})$ |
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299 %% \item $(i\implies i+1)$ |
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300 %% \item Repeat from 2 for as long as you want |
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301 %% \end{enumerate} |
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302 %% \inctime{20} |
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303 %% \end{frame} |