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21 |
21 |
22 \usepackage[english]{babel} |
22 \usepackage[english]{babel} |
23 \usepackage[latin1]{inputenc} |
23 \usepackage[latin1]{inputenc} |
24 %\usepackage{times} |
24 %\usepackage{times} |
25 \usepackage[T1]{fontenc} |
25 \usepackage[T1]{fontenc} |
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26 \usepackage{amsmath} |
26 |
27 |
27 % Taken from Fernando's slides. |
28 % Taken from Fernando's slides. |
28 \usepackage{ae,aecompl} |
29 \usepackage{ae,aecompl} |
29 \usepackage{mathpazo,courier,euler} |
30 \usepackage{mathpazo,courier,euler} |
30 \usepackage[scaled=.95]{helvet} |
31 \usepackage[scaled=.95]{helvet} |
118 \end{frame} |
119 \end{frame} |
119 |
120 |
120 \begin{frame} |
121 \begin{frame} |
121 \frametitle{Outline} |
122 \frametitle{Outline} |
122 \tableofcontents |
123 \tableofcontents |
123 \pausesections |
124 % \pausesections |
124 \end{frame} |
125 \end{frame} |
125 |
126 |
126 \section{Matrices} |
127 \section{Matrices} |
127 \subsection{Initializing} |
128 \subsection{Initializing} |
128 \begin{frame}[fragile] |
129 \begin{frame}[fragile] |
181 [-0.52532209, -0.08675134, -0.81649658], |
182 [-0.52532209, -0.08675134, -0.81649658], |
182 [-0.8186735 , 0.61232756, 0.40824829]])) |
183 [-0.8186735 , 0.61232756, 0.40824829]])) |
183 \end{lstlisting} |
184 \end{lstlisting} |
184 \end{frame} |
185 \end{frame} |
185 |
186 |
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187 \begin{frame}[fragile] |
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188 \frametitle{ODE Integration} |
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189 We shall use the simple ODE of a simple pendulum. |
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190 \begin{equation*} |
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191 \ddot{\theta} = -\frac{g}{L}sin(\theta) |
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192 \end{equation*} |
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193 \begin{itemize} |
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194 \item This equation can be written as a system of two first order ODEs |
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195 \item $\dot{\theta} = \omega$ |
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196 \item $\dot{\omega} = -\frac{g}{L}sin(\theta)$ |
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197 \item At $t = 0$ \\ |
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198 $\theta = \theta_0$ \& |
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199 $\omega = 0$ |
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200 \end{itemize} |
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201 \begin{lstlisting} |
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202 \end{lstlisting} |
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203 \end{frame} |
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204 |
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205 |
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206 |
186 \end{document} |
207 \end{document} |
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208 |
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209 \begin{frame}[fragile] |
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210 \frametitle{} |
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211 \begin{lstlisting} |
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212 \end{lstlisting} |
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213 \end{frame} |