Definition:Complex Curvilinear Coordinates/Coordinate Curves

Definition

Let $u + i v = \map f {x + i y}$ be a complex transformation.

Let $c_1$ and $c_2$ be constants.

The curves:

$\map u {x, y} = c_1$

$\map v {x, y} = c_2$

are the coordinate curves of $f$.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: Curvilinear Coordinates