\item Consider a flat 2D plane mapped by the standard polar coordinates.
  \begin{enumerate}[label=(\alph*)]
    \item Write down $ds^2$.
    \item What are the coefficients $g_{ij}$?
    \item What are the coefficients $g^{ij}$?
    \item Calculate the Christoffel symbols for this system.
    \item Using
          $$
          \dot{x}^\lambda+\Gamma^\lambda_{\mu\nu}\dot{x}^\mu\dot{x}^\nu=0
          $$
          derive the two coupled, second-order differential equations
          that describe the motion of a free particle in this system.
  \end{enumerate}