\section{Exercises}
\begin{footnotesize} 
\subsection*{Targeted exercises} 
\subsubsection*{Exercises for Section \ref{Implementing_linear_interpolation_using_numpy.interp}} 
\begin{enumerate}\setcounter{enumi}{-1}
	\item  Consider a Gaussian distribution with $x_0 = 0$, $\sigma = 2$, and amplitude of 1. 
    \begin{itemize}
        \item Create 1000 $x$-values between -10 and 10, and use this to create y-values with the above Gaussian parameters. This will represent the `true' Guassian shape. 
	\item Repeat the above, but with  5, 6, 7, 8, 9, 10, 11, 12 points, each from -10 and 10. These will represent sparsely sampled points.
	\item For each set of points generated in the second step, perform a linear interpolation using \lstinline{numpy.interp()}. This accepts three positional arguments: an array of $x$-values you wisht to generate interpolated points for, the original $x$-values, and the original $y$ values used for interpolation.
	\item  Make a Plotly plot holding a separate subplot for each of the eight sparse arrays. On this plot, have the `true' Gaussian shape, the sparsely sampled points, and the interpolated values.
	\item  Comment on how the interpolation improves with sample points. 
	\item  Comment on what regions of the Gaussian seem to be reproduced well, and which are not. 
    \end{itemize}
\end{enumerate}


\subsubsection*{Exercises for Section \ref{Implementing_cubic_spline_interpolation_using_scipy.interpolate.CubicSpline}} 
\begin{enumerate}\setcounter{enumi}{0}
	\item  Repeat Exercise 0, but use a cubic spline for interpolation. 

    In addition to answering all parts from Exercise 0, comment on the differences between the results from the linear interpolation, versus the cubic interpolation.

	
\end{enumerate}
\subsection*{Comprehensive} 
\begin{enumerate}\setcounter{enumi}{1}
	\item  Modify the final code from Chapter 8 to interpolate the kinetic traces so that they have evenly spaced points.  Use both linear interpolation and cubic splines.  Do you notice any obvious inaccuracies for either method?

\end{enumerate}
\end{footnotesize} 
