equal
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inserted
replaced
196 \end{frame} |
196 \end{frame} |
197 |
197 |
198 \begin{frame}[fragile] |
198 \begin{frame}[fragile] |
199 \frametitle{Initial Estimates} |
199 \frametitle{Initial Estimates} |
200 \begin{itemize} |
200 \begin{itemize} |
201 \item Find the roots of $cosx-x^2$ between $-\pi/2$ and $\pi/2$ |
201 \item Find roots of $cosx-x^2$ in $(-\pi/2, \pi/2)$ |
202 \item We shall use a crude method to get an initial estimate first |
202 \item How to get a rough initial estimate? |
203 \end{itemize} |
203 \end{itemize} |
204 \begin{enumerate} |
204 \begin{enumerate} |
205 \item Check for change of signs of $f(x)$ in the given interval |
205 \item Check for change of signs of $f(x)$ in the given interval |
206 \item A root lies in the interval where the sign change occurs |
206 \item A root lies in the interval where the sign change occurs |
207 \end{enumerate} |
207 \end{enumerate} |
348 \end{lstlisting} |
348 \end{lstlisting} |
349 \end{frame} |
349 \end{frame} |
350 |
350 |
351 \begin{frame}[fragile] |
351 \begin{frame}[fragile] |
352 \frametitle{Scipy Methods \dots} |
352 \frametitle{Scipy Methods \dots} |
353 \small{ |
353 \begin{small} |
354 \begin{lstlisting} |
354 \begin{lstlisting} |
355 In []: from scipy.optimize import fixed_point |
355 In []: from scipy.optimize import fixed_point |
356 |
356 |
357 In []: from scipy.optimize import bisect |
357 In []: from scipy.optimize import bisect |
358 |
358 |
359 In []: from scipy.optimize import newton |
359 In []: from scipy.optimize import newton |
360 \end{lstlisting}} |
360 \end{lstlisting} |
361 \end{frame} |
361 \end{small} |
362 |
362 \end{frame} |
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363 |
|
364 \begin{frame} |
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365 \frametitle{Things we have learned} |
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366 \begin{itemize} |
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367 \item Solving ODEs |
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368 \item Finding Roots |
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369 \begin{itemize} |
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370 \item Estimating Interval |
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371 \item Newton Raphson |
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372 \item Scipy methods |
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373 \end{itemize} |
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374 \end{itemize} |
|
375 \end{frame} |
363 |
376 |
364 \end{document} |
377 \end{document} |