Definition:Contour/Closed/Complex Plane

Definition
Let $C$ be a contour in $\C$ defined by the (finite) sequence $\left\langle{C_1, \ldots, C_n}\right\rangle$ of directed smooth curves in $\C$.

Let $C_i$ be parameterized by the smooth path $\gamma_i: \left[{a_i \,.\,.\, b_i}\right] \to \C$ for all $i \in \left\{ {1, \ldots, n}\right\}$.

$C$ is a closed contour the start point of $C$ is equal to the endpoint of $C$:


 * $\gamma_1 \left({a_1}\right) = \gamma_n \left({b_n}\right)$

Also see

 * Reparameterization of Directed Smooth Curve Maps Endpoints To Endpoints, from which it follows that this definition is independent of the parameterizations of $C_1$ and $C_n$.

Also known as
A closed contour is called a loop in some texts.

Some texts define a contour to be what refers to as a closed contour.