Complex Analysis/Trace

Definition

A curve in

$ℂ$

is a continuous mapping

$\gamma :[a,b]\to ℂ$

. The image set

$\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{e}(\gamma ):=\{\gamma (t):t\in [a,b]\}$

is called the "trace" of the curve.

Properties of Curves

• A curve is called differentiable, $C^k$, etc., if the defining mapping has these properties.
• A property particularly important for the theory of Curve Integral is therectifiable curve rectifiable of a curve, rectifiable curves are curves over which integration is possible.

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