Category:Fundamental Theorem of Calculus for Contour Integrals

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This category contains pages concerning Fundamental Theorem of Calculus for Contour Integrals:


Let $F, f: D \to \C$ be complex functions, where $D$ is a connected domain.

Let $C$ be a contour that is a concatenation of the directed smooth curves $C_1, \ldots, C_n$.

Let $C_k$ be parameterized by the smooth path $\gamma_k: \closedint {a_k} {b_k} \to D$ for all $k \in \set {1, \ldots, n}$.


Suppose that $F$ is an antiderivative of $f$.


If $C$ has start point $z$ and end point $w$, then:

$\ds \int_C \map f z \rd z = \map F w - \map F z$


If $C$ is a closed contour, then:

$\ds \oint_C \map f z \rd z = 0$

Pages in category "Fundamental Theorem of Calculus for Contour Integrals"

The following 2 pages are in this category, out of 2 total.