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{\large Astro 321: CMB Final Helper Problem Set 2}
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\noindent{\large\bf Spline Interpolation}
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\begin{itemize}
\item{} Go to {\tt http://www.nr.com}, download chapter 3.3 and read the
section on spline interpolation.
\item{} Familiarize yourself with the use of their "spline" and "splint"
routines.
\item{} Take the $\eta(a)$ output of the Runge-Kutta test and spline interpolate
to find the value at some $a$ that is not at an output time, e.g. $a=0.001234$.
"Spline invert" the relation and find $a(\eta)$ at some $\eta$ say
$100$ Mpc. Check your answers against the analytic result.
\item{} Write these spline interpolation routines as a piece of modular code
so that your Boltzmann code can efficiently convert between $a$ and $\eta$.
This is not strictly necessary for a matter-radiation universe where analytic
solutions are available but will come in handy if you want to generalize
your code.
\end{itemize}
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