equal
deleted
inserted
replaced
283 %% ....: |
283 %% ....: |
284 %% \end{lstlisting} |
284 %% \end{lstlisting} |
285 %% \end{frame} |
285 %% \end{frame} |
286 |
286 |
287 \begin{frame}[fragile] |
287 \begin{frame}[fragile] |
288 \frametitle{Newton Raphson Method} |
288 \frametitle{Newton-Raphson Method} |
289 \begin{enumerate} |
289 \begin{enumerate} |
290 \item Start with an initial guess of x for the root |
290 \item Start with an initial guess of x for the root |
291 \item $\Delta x = -f(x)/f^{'}(x)$ |
291 \item $\Delta x = -f(x)/f^{'}(x)$ |
292 \item $ x \leftarrow x + \Delta x$ |
292 \item $ x \leftarrow x + \Delta x$ |
293 \item Go back to 2 until $|\Delta x| \le$ tolerance |
293 \item Go back to 2 until $|\Delta x| \le$ tolerance |
294 \end{enumerate} |
294 \end{enumerate} |
295 \end{frame} |
295 \end{frame} |
296 |
296 |
297 %% \begin{frame}[fragile] |
297 %% \begin{frame}[fragile] |
298 %% \frametitle{Newton Raphson \dots} |
298 %% \frametitle{Newton-Raphson \dots} |
299 %% \begin{lstlisting} |
299 %% \begin{lstlisting} |
300 %% In []: def our_df(x): |
300 %% In []: def our_df(x): |
301 %% ....: return -sin(x)-2*x |
301 %% ....: return -sin(x)-2*x |
302 %% ....: |
302 %% ....: |
303 %% In []: delx = 10*tolerance |
303 %% In []: delx = 10*tolerance |
308 %% ....: |
308 %% ....: |
309 %% \end{lstlisting} |
309 %% \end{lstlisting} |
310 %% \end{frame} |
310 %% \end{frame} |
311 |
311 |
312 \begin{frame}[fragile] |
312 \begin{frame}[fragile] |
313 \frametitle{Newton Raphson \ldots} |
313 \frametitle{Newton-Raphson \ldots} |
314 \begin{itemize} |
314 \begin{itemize} |
315 \item What if $f^{'}(x) = 0$? |
315 \item What if $f^{'}(x) = 0$? |
316 \item Can you write a better version of the Newton Raphson? |
316 \item Can you write a better version of the Newton-Raphson? |
317 \item What if the differential is not easy to calculate? |
317 \item What if the differential is not easy to calculate? |
318 \item Look at Secant Method |
318 \item Look at Secant Method |
319 \end{itemize} |
319 \end{itemize} |
320 \end{frame} |
320 \end{frame} |
321 |
321 |
366 \begin{itemize} |
366 \begin{itemize} |
367 \item Solving ODEs |
367 \item Solving ODEs |
368 \item Finding Roots |
368 \item Finding Roots |
369 \begin{itemize} |
369 \begin{itemize} |
370 \item Estimating Interval |
370 \item Estimating Interval |
371 \item Newton Raphson |
371 \item Newton-Raphson |
372 \item Scipy methods |
372 \item Scipy methods |
373 \end{itemize} |
373 \end{itemize} |
374 \end{itemize} |
374 \end{itemize} |
375 \end{frame} |
375 \end{frame} |
376 |
376 |