Definition:Reversed Contour

Definition

Let $C$ be a contour in $\R^n$.

Then $C$ is defined as a concatenation of a finite sequence $C_1, \ldots, C_n$ of directed smooth curves in $\R^n$.

The reversed contour of $C$ is denoted $-C$ and is defined as the concatenation of the finite sequence:

$-C_n, -C_{n - 1}, \ldots, -C_1$

where $-C_i$ is the reversed directed smooth curve of $C_i$ for all $i \in \set {1, \ldots, n}$.

The definition carries over to the complex plane, in which context it is usually applied:

Let $C$ be a contour in the complex plane $\C$.

Then $C$ is defined as a concatenation of a finite sequence $\sequence {C_1, \ldots, C_n}$ of directed smooth curves in $\C$.

The reversed contour of $C$ is denoted $-C$ and is defined as the concatenation of the finite sequence:

$-C_n, -C_{n-1}, \ldots, -C_1$

where $-C_k$ is the reversed directed smooth curve of $C_k$ for all $i \in \set {1, \ldots, n}$.

The reversed contour of $C$ is denoted as $C^-$ in some texts.