Definition:Contour/Endpoints/Complex Plane
< Definition:Contour | Endpoints(Redirected from Definition:Start Point of Contour (Complex Plane))
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Definition
Let $C_1, \ldots, C_n$ be directed smooth curves in $\C$.
Let $C_k$ be parameterized by the smooth path $\gamma_k: \closedint {a_k}{b_k} \to \C$ for all $k \in \set{ 1, \ldots, n}$.
Let $C$ be the contour defined by the finite sequence $\sequence {C_1, \ldots, C_n}$.
The start point of $C$ is $\map {\gamma_1}{a_1}$.
The end point of $C$ is $\map {\gamma_n}{b_n}$.
Collectively, $\map {\gamma_1}{a_1}$ and $\map {\gamma_n}{b_n}$ are referred to as the endpoints of $C$.
Also see
From Reparameterization of Directed Smooth Curve Maps Endpoints To Endpoints, it follows that this definition is independent of the parameterizations of $C_1, \ldots, C_n$.
Sources
- 2001: Christian Berg: Kompleks funktionsteori $\S 2.2$