Math 6420 • PDE

\begin{enumerate}
\item[(a)] Consider a 2-dimensional map \((x,y)\to(u,v)\). Explain: If the map is given by
an analytic function [\(u+iv=f(x+iy)\)] and at some point \(z_0=x_0+iy_0\) the derivative
\(f'(z_0)\ne0\), then this map preserves small shapes in the vicinity of \(z_0\).

\item[(b)] Is a square conformally equivalent to a circle?

\item[(c)] Explain: A map by analytic function preserves Laplace's equation.
\end{enumerate}