Continuous Jordan curve & Contour.

𝑪𝒐𝒎𝒑𝒍𝒆𝒙 𝑨𝒏𝒂𝒍𝒚𝒔𝒊𝒔 𝑻𝒉𝒆𝒐𝒓𝒆𝒎 𝒇𝒓𝒐𝒎 𝑪𝒐𝒎𝒑𝒍𝒆𝒙 𝑰𝒏𝒕𝒆𝒈𝒓𝒂𝒕𝒊𝒐𝒏

Continuous Jordan curve & Contour

Continuous Jordan Curve:-

A continuous Jordan curve consist of a chain of finite no of continuous Arc.

Contour :-

A Jordan curve consisting of continuous chain of a finite no of regular Arc is known as contour.
If 𝑨 be the starting point of the first Arc and 𝑩 be the end point of the last Arc then integral along such a curve is written as
∫꜀ 𝑓(𝑧)𝑑𝑧 . Here 𝑐 is a curve 𝑨𝑩.

If the starting point 𝑨 of the arc concides with the end point 𝑩 of the last arc, then the Contour 𝑨𝑩 is said to be closed and the integral along such closed contour is written as ∫꜀ 𝑓(𝑧)𝑑𝑧,
And this is read as integral 𝑓 (𝑧) taken over the closed contour 𝑪.
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#complexanalysis #csirnet #complexintegration #jordanarc #riemannintegral

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