Category:Definitions/Complex Contour Integrals
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This category contains definitions related to Complex Contour Integrals.
Related results can be found in Category:Complex Contour Integrals.
Let $C$ be a contour defined by a finite sequence $C_1, \ldots, C_n$ of directed smooth curves in the complex plane $\C$.
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 $f: \Img C \to \C$ be a continuous complex function, where $\Img C$ denotes the image of $C$.
The contour integral of $f$ along $C$ is defined by:
- $\ds \int_C \map f z \rd z = \sum_{k \mathop = 1}^n \int_{a_k}^{b_k} \map f {\map {\gamma_k} t} \map {\gamma_k'} t \rd t$
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Pages in category "Definitions/Complex Contour Integrals"
The following 4 pages are in this category, out of 4 total.