User talk:Egm6321.f10.team5.steinberg/hw6

Part 1
From the Wikipedia article, the elliptic coordinates are defined as shown in (7.1) and (7.2).

Part 3
For orthogonal curvilinear coordinates (2D), the Laplacian operator may be defined as

Since $$ h_1 $$ and $$ h_2 $$ are equal, (7.10) becomes