336 \begin{frame}[fragile]

   336 \begin{frame}[fragile]

   337   \frametitle{Integrate \ldots}

   337   \frametitle{Integrate \ldots}

   338   Numerically solve ODEs\\

   338   Numerically solve ODEs\\

   339   \begin{align*}

   339   \begin{align*}

   340   \frac{dx}{dt}&=-e^{-t}x^2\\ 

   340   \frac{dx}{dt}&=-e^{-t}x^2\\ 

   342   \end{align*}

   342   \end{align*}

   343   \begin{lstlisting}

   343   \begin{lstlisting}

   344 >>> def dx_dt(x,t):

   344 >>> def dx_dt(x,t):

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

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

   347 >>> x=integrate.odeint(dx_dt, 2, t)

   347 >>> x=integrate.odeint(dx_dt, 2, t)

   348 >>> plt.plot(x,t)

   348 >>> plt.plot(x,t)

   349   \end{lstlisting}

   349   \end{lstlisting}

   350 \inctime{10}

   350 \inctime{10}

   351 \end{frame}

   351 \end{frame}

   370 

   370 

   371 \begin{frame}[fragile]

   371 \begin{frame}[fragile]

   372   \frametitle{Interpolation - Splines}

   372   \frametitle{Interpolation - Splines}

   373   Plot the Cubic Spline of $sin(x)$

   373   Plot the Cubic Spline of $sin(x)$

   374   \begin{lstlisting}

   374   \begin{lstlisting}

   377 >>> tck = interpolate.splrep(x,y)

   375 >>> tck = interpolate.splrep(x,y)

   378 >>> X = np.arange(0,2*np.pi,np.pi/50)

   376 >>> X = np.arange(0,2*np.pi,np.pi/50)

   379 >>> Y = interpolate.splev(X,tck,der=0)

   377 >>> Y = interpolate.splev(X,tck,der=0)

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

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

   381 >>> plt.show()

   379 >>> plt.show()