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234 [-0.52532209, -0.08675134, -0.81649658], |
234 [-0.52532209, -0.08675134, -0.81649658], |
235 [-0.8186735 , 0.61232756, 0.40824829]])) |
235 [-0.8186735 , 0.61232756, 0.40824829]])) |
236 \end{lstlisting} |
236 \end{lstlisting} |
237 \end{small} |
237 \end{small} |
238 \end{frame} |
238 \end{frame} |
239 |
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240 |
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241 \section{Integration} |
239 \section{Integration} |
242 |
240 |
243 \subsection{Quadrature} |
241 \subsection{Quadrature} |
244 |
242 |
245 \begin{frame}[fragile] |
243 \begin{frame}[fragile] |
249 \item Area under $(sin(x) + x^2)$ in $(0,1)$ |
247 \item Area under $(sin(x) + x^2)$ in $(0,1)$ |
250 \item scipy has functions to do that |
248 \item scipy has functions to do that |
251 \end{itemize} |
249 \end{itemize} |
252 \small{\typ{In []: from scipy.integrate import quad}} |
250 \small{\typ{In []: from scipy.integrate import quad}} |
253 \begin{itemize} |
251 \begin{itemize} |
254 \item Inputs - function to integrate, limits |
252 \item Inputs - function to integrate, limits of integration |
255 \end{itemize} |
253 \end{itemize} |
256 \begin{lstlisting} |
254 \begin{lstlisting} |
257 In []: x = 0 |
255 In []: x = 0 |
258 In []: quad(sin(x)+x**2, 0, 1) |
256 In []: quad(sin(x)+x**2, 0, 1) |
259 \end{lstlisting} |
257 \end{lstlisting} |
349 |
347 |
350 \subsection{ODEs} |
348 \subsection{ODEs} |
351 |
349 |
352 \begin{frame}[fragile] |
350 \begin{frame}[fragile] |
353 \frametitle{ODE Integration} |
351 \frametitle{ODE Integration} |
354 We shall use the simple ODE of a simple pendulum. |
352 We shall look at the motion of a simple pendulum. |
355 \begin{equation*} |
353 \begin{equation*} |
356 \ddot{\theta} = -\frac{g}{L}sin(\theta) |
354 \ddot{\theta} = -\frac{g}{L}sin(\theta) |
357 \end{equation*} |
355 \end{equation*} |
358 \begin{itemize} |
356 \begin{itemize} |
359 \item This equation can be written as a system of two first order ODEs |
357 \item This equation can be written as a system of two first order ODEs |