Revision as of 07:13, 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 $\Omega$ , and let $\gamma$ be a nullhomologous, piecewise $$ C^1 $$ curve in $\Omega$ . Then

$\int_\gamma f(z)\, dz =0$

@@ Line 7: / Line 7: @@
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-<math>\mathrm{\underline{Cauchy's theorem}: Let } f:\mathbb{C} \to \mathbb{C}</math>
+<u>Cauchy's theorem:</u> Let f be analytic on a domain <math>\Omega</math>, and let <math>\gamma</math> be a nullhomologous, piecewise&nbsp;<math>C^1</math> curve in <math>\Omega</math>.&nbsp; Then
-<br>
+<math>\int_\gamma f(z)\, dz =0</math>
 <br> [[2014 Summer MA 598C Weigel|Back to 2014 Summer MA 598C Weigel]]
 [[Category:2014_Summer_MA_598C_Weigel]]