181            [7, 8, 9]])

   181            [7, 8, 9]])

   182   \end{lstlisting}

   182   \end{lstlisting}

   183   \begin{itemize}

   183   \begin{itemize}

   184   \item Index arrays or Boolean arrays produce copies

   184   \item Index arrays or Boolean arrays produce copies

   185   \end{itemize}

   185   \end{itemize}

   186 \end{frame}

   187 \end{frame}

   187 

   188 

   188 \begin{frame}

   189 \begin{frame}

   189   \frametitle{More Numpy Functions \& Methods}

   190   \frametitle{More Numpy Functions \& Methods}

   190   More functions

   191   More functions

   252     -x + \frac{1}{2}y -z & = 0

   253     -x + \frac{1}{2}y -z & = 0

   253   \end{align*}

   254   \end{align*}

   254   \begin{lstlisting}

   255   \begin{lstlisting}

   255     >>> linalg.solve(A,B)

   256     >>> linalg.solve(A,B)

   256   \end{lstlisting}

   257   \end{lstlisting}

   257 \end{frame}

   259 \end{frame}

   258 

   260 

   259 \begin{frame}[fragile]

   261 \begin{frame}[fragile]

   260   \begin{itemize}

   262   \begin{itemize}

   261     \item Integrating Functions given function object

   263     \item Integrating Functions given function object

   283         return -np.exp(-t)*x**2

   285         return -np.exp(-t)*x**2

   284 

   286 

   285     x=integrate.odeint(dx_dt, 2, t)

   287     x=integrate.odeint(dx_dt, 2, t)

   286     plt.plot(x,t)

   288     plt.plot(x,t)

   287   \end{lstlisting}

   289   \end{lstlisting}

   288 \end{frame}

   291 \end{frame}

   289 

   292 

   290 \begin{frame}[fragile]

   293 \begin{frame}[fragile]

   291   \frametitle{Interpolation}

   294   \frametitle{Interpolation}

   292   \begin{itemize}

   295   \begin{itemize}

   302     Y = interpolate.splev(X,t,der=0)

   305     Y = interpolate.splev(X,t,der=0)

   303 

   306 

   304     plt.plot(x,y,'o',x,y,X,Y)

   307     plt.plot(x,y,'o',x,y,X,Y)

   305     plt.show()

   308     plt.show()

   306   \end{lstlisting}

   309   \end{lstlisting}

   307 \end{frame}

   311 \end{frame}

   308 

   312 

   309 \begin{frame}[fragile]

   313 \begin{frame}[fragile]

   310   \frametitle{Signal \& Image Processing}

   314   \frametitle{Signal \& Image Processing}

   311     \begin{itemize}

   315     \begin{itemize}

   334   \end{lstlisting}

   338   \end{lstlisting}

   335   Zooming an array - uses spline interpolation

   339   Zooming an array - uses spline interpolation

   336   \begin{lstlisting}

   340   \begin{lstlisting}

   337     b=ndimage.zoom(A,0.5)

   341     b=ndimage.zoom(A,0.5)

   338     imshow(b)

   342     imshow(b)

   339   \end{lstlisting}

   344   \end{lstlisting}

   340 

   345 

   341 \end{frame}

   346 \end{frame}

   342 

   347 

   343 \begin{frame}[fragile]

   348 \begin{frame}[fragile]

   344   \frametitle{Problems}

   349   \frametitle{Problems}

   345   The Van der Pol oscillator is a type of nonconservative oscillator with nonlinear damping. It evolves in time according to the second order differential equation:

   350   The Van der Pol oscillator is a type of nonconservative oscillator with nonlinear damping. It evolves in time according to the second order differential equation:

   346   \begin{equation*}

   351   \begin{equation*}

   347   \frac{d^2x}{dt^2}+\mu(x^2-1)\frac{dx}{dt}+x= 0

   352   \frac{d^2x}{dt^2}+\mu(x^2-1)\frac{dx}{dt}+x= 0

   348   \end{equation*}

   353   \end{equation*}

   349 \end{frame}

   355 \end{frame}

   350 

   356 

   351 

   357 

   352 \end{document}

   358 \end{document}

   353 

   359