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what is the cauchy-coursat theorem state specifically in word? Is it calculate the area or the legth,which area and what legth? please give a example! And what is deformation of contour?

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You probably mean Cauchy-Goursat. Did you ask google? Clicking this link should give you quite a few hits. –  t.b. Jul 10 '11 at 20:12
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Deformation of contour refers to homotopy. This whole machinery is dealt with nicely in John Conway's complex analysis book. –  ncmathsadist Jul 10 '11 at 20:27

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up vote 1 down vote accepted

http://en.wikipedia.org/wiki/Cauchy-Goursat_theorem

Contour integrals in the complex plane can't be interpreted in terms of length or area.

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But why is it represent as number? –  Victor Jul 10 '11 at 21:01

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