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253 \begin{itemize} |
253 \begin{itemize} |
254 \item Inputs - function to integrate, limits |
254 \item Inputs - function to integrate, limits |
255 \end{itemize} |
255 \end{itemize} |
256 \begin{lstlisting} |
256 \begin{lstlisting} |
257 In []: x = 0 |
257 In []: x = 0 |
258 In []: integrate.quad(sin(x)+x**2, 0, 1) |
258 In []: quad(sin(x)+x**2, 0, 1) |
259 \end{lstlisting} |
259 \end{lstlisting} |
260 \alert{\typ{error:}} |
260 \alert{\typ{error:}} |
261 \typ{First argument must be a callable function.} |
261 \typ{First argument must be a callable function.} |
262 \end{frame} |
262 \end{frame} |
263 |
263 |
264 \begin{frame}[fragile] |
264 \begin{frame}[fragile] |
265 \frametitle{Functions - Definition} |
265 \frametitle{Functions - Definition} |
266 \begin{lstlisting} |
266 \begin{lstlisting} |
267 In []: def f(x): |
267 In []: def f(x): |
268 return sin(x)+x**2 |
268 return sin(x)+x**2 |
269 In []: integrate.quad(f, 0, 1) |
269 In []: quad(f, 0, 1) |
270 \end{lstlisting} |
270 \end{lstlisting} |
271 \begin{itemize} |
271 \begin{itemize} |
272 \item \typ{def} |
272 \item \typ{def} |
273 \item arguments |
273 \item arguments |
274 \item \typ{return} |
274 \item \typ{return} |
336 \end{frame} |
336 \end{frame} |
337 |
337 |
338 \begin{frame}[fragile] |
338 \begin{frame}[fragile] |
339 \frametitle{Quadrature \ldots} |
339 \frametitle{Quadrature \ldots} |
340 \begin{lstlisting} |
340 \begin{lstlisting} |
341 In []: integrate.quad(f, 0, 1) |
341 In []: quad(f, 0, 1) |
342 \end{lstlisting} |
342 \end{lstlisting} |
343 Returns the integral and an estimate of the absolute error in the result. |
343 Returns the integral and an estimate of the absolute error in the result. |
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344 \begin{itemize} |
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345 \item Use \typ{dblquad} for Double integrals |
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346 \item Use \typ{tplquad} for Triple integrals |
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347 \end{itemize} |
344 \end{frame} |
348 \end{frame} |
345 |
349 |
346 \subsection{ODEs} |
350 \subsection{ODEs} |
347 |
351 |
348 \begin{frame}[fragile] |
352 \begin{frame}[fragile] |
401 initial,t, |
405 initial,t, |
402 args=(p,)) |
406 args=(p,)) |
403 \end{lstlisting} |
407 \end{lstlisting} |
404 \end{frame} |
408 \end{frame} |
405 |
409 |
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410 \begin{frame} |
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411 \frametitle{Things we have learned} |
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412 \begin{itemize} |
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413 \item |
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414 \item |
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415 \item Functions |
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416 \begin{itemize} |
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417 \item Definition |
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418 \item Calling |
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419 \item Default Arguments |
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420 \item Keyword Arguments |
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421 \end{itemize} |
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422 \item Integration |
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423 \begin{itemize} |
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424 \item Quadrature |
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425 \item ODEs |
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426 \end{itemize} |
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427 \end{itemize} |
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428 \end{frame} |
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429 |
406 \end{document} |
430 \end{document} |
407 |
431 |