94 \frametitle{Outline} |
94 \frametitle{Outline} |
95 \tableofcontents[currentsection,currentsubsection] |
95 \tableofcontents[currentsection,currentsubsection] |
96 \end{frame} |
96 \end{frame} |
97 } |
97 } |
98 |
98 |
99 %%\AtBeginSection[] |
99 \AtBeginSection[] |
100 %%{ |
100 { |
101 %%\begin{frame}<beamer> |
101 \begin{frame}<beamer> |
102 %% \frametitle{Outline} |
102 \frametitle{Outline} |
103 %% \tableofcontents[currentsection,currentsubsection] |
103 \tableofcontents[currentsection,currentsubsection] |
104 %%\end{frame} |
104 \end{frame} |
105 %%} |
105 } |
106 |
106 |
107 % If you wish to uncover everything in a step-wise fashion, uncomment |
107 % If you wish to uncover everything in a step-wise fashion, uncomment |
108 % the following command: |
108 % the following command: |
109 %\beamerdefaultoverlayspecification{<+->} |
109 %\beamerdefaultoverlayspecification{<+->} |
110 |
110 |
216 #use der=1, 2,.. for 1st, 2nd,.. order |
216 #use der=1, 2,.. for 1st, 2nd,.. order |
217 In []: Tnew = splev(Lnew, tck, der=1) |
217 In []: Tnew = splev(Lnew, tck, der=1) |
218 \end{lstlisting} |
218 \end{lstlisting} |
219 \end{frame} |
219 \end{frame} |
220 |
220 |
221 \begin{frame}[fragile] |
221 %% \begin{frame}[fragile] |
222 \frametitle{} |
222 %% \frametitle{Interpolation \ldots} |
223 \end{frame} |
223 %% \begin{itemize} |
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224 %% \item |
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225 %% \end{itemize} |
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226 %% \end{frame} |
224 |
227 |
225 \section{Differentiation} |
228 \section{Differentiation} |
226 |
229 |
227 \begin{frame}[fragile] |
230 \begin{frame}[fragile] |
228 \frametitle{Numerical Differentiation} |
231 \frametitle{Numerical Differentiation} |
259 \includegraphics[height=2in, interpolate=true]{data/fwdDiff} |
262 \includegraphics[height=2in, interpolate=true]{data/fwdDiff} |
260 \end{center} |
263 \end{center} |
261 \end{frame} |
264 \end{frame} |
262 |
265 |
263 \begin{frame}[fragile] |
266 \begin{frame}[fragile] |
264 \frametitle{} |
267 \frametitle{Example} |
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268 \begin{itemize} |
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269 \item Given x, y positions of a particle in \typ{pos.txt} |
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270 \item Find velocity \& acceleration in x, y directions |
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271 \end{itemize} |
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272 \small{ |
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273 \begin{center} |
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274 \begin{tabular}{| c | c | c |} |
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275 \hline |
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276 $X$ & $Y$ \\ \hline |
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277 0. & 0.\\ \hline |
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278 0.25 & 0.47775\\ \hline |
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279 0.5 & 0.931\\ \hline |
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280 0.75 & 1.35975\\ \hline |
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281 1. & 1.764\\ \hline |
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282 1.25 & 2.14375\\ \hline |
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283 \vdots & \vdots\\ \hline |
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284 \end{tabular} |
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285 \end{center}} |
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286 \end{frame} |
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287 |
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288 \begin{frame}[fragile] |
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289 \frametitle{Example \ldots} |
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290 \begin{itemize} |
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291 \item Read the file |
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292 \item Obtain an array of x, y |
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293 \item Obtain velocity and acceleration |
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294 \item use \typ{deltaT = 0.05} |
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295 \end{itemize} |
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296 \begin{lstlisting} |
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297 In []: X = [] |
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298 In []: Y = [] |
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299 In []: for line in open('location.txt'): |
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300 .... points = line.split() |
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301 .... X.append(float(points[0])) |
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302 .... Y.append(float(points[1])) |
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303 In []: S = array([X, Y]) |
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304 \end{lstlisting} |
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305 \end{frame} |
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306 |
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307 |
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308 \begin{frame}[fragile] |
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309 \frametitle{Example \ldots} |
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310 \begin{itemize} |
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311 \item use \typ{deltaT = 0.05} |
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312 \end{itemize} |
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313 \begin{lstlisting} |
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314 In []: deltaT = 0.05 |
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315 |
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316 In []: v = (S[:,1:]-S[:,:-1])/deltaT |
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317 |
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318 In []: a = (v[:,1:]-v[:,:-1])/deltaT |
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319 \end{lstlisting} |
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320 Try Plotting the position, velocity \& acceleration. |
265 \end{frame} |
321 \end{frame} |
266 |
322 |
267 \section{Quadrature} |
323 \section{Quadrature} |
268 |
324 |
269 \begin{frame}[fragile] |
325 \begin{frame}[fragile] |