Category:Definitions/Contours

This category contains definitions related to Contours.
Related results can be found in Category:Contours.

Let $\R^n$ be a real cartesian space of $n$ dimensions.

Let $C_1, \ldots, C_n$ be directed smooth curves in $\R^n$.

For each $i \in \set {1, \ldots, n}$, let $C_i$ be parameterized by the smooth path $\rho_i: \closedint {a_i} {b_i} \to \R^n$.

For each $i \in \set {1, \ldots, n - 1}$, let the end point of $\rho_i$ equal the start point of $\rho_{i + 1}$:

$\map {\rho_i} {b_i} = \map {\rho_{i + 1} } {a_{i + 1} }$

Then the finite sequence $\sequence {C_1, \ldots, C_n}$ is called a contour (in $\R^n$).