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<u>Cauchy's theorem:</u> Let f be analytic on a domain <span class="texhtml">Ω</span>, and let <span class="texhtml">γ</span> be a nullhomologous, piecewise&nbsp;<span class="texhtml">''C''<sup>1</sup></span> curve in <span class="texhtml">Ω</span>.&nbsp; Then<math>\int_\gamma f(z)\, dz =0</math>  
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<u>Cauchy's theorem:</u> Let f be analytic on a domain <span class="texhtml">Ω</span>, and let <span class="texhtml">γ</span> be a nullhomologous, piecewise&nbsp;<span class="texhtml">''C''<sup>1</sup></span> curve in <span class="texhtml">Ω</span>.&nbsp; Then&nbsp;<math>\int_\gamma f(z)\,dz =0.</math>  
  
 
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[[Category:2014_Summer_MA_598C_Weigel]]

Latest revision as of 07:14, 5 August 2014


Really important results

Be able to state these perfectly, while taking a nap and juggling chainsaws.


Cauchy's theorem: Let f be analytic on a domain Ω, and let γ be a nullhomologous, piecewise C1 curve in Ω.  Then $ \int_\gamma f(z)\,dz =0. $


Back to 2014 Summer MA 598C Weigel

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang