Latest revision as of 06:14, 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 $C 1$ curve in $Ω$ . Then $\int_\gamma f(z)\,dz =0.$

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-<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
+<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>
-<math>\int_\gamma f(z)\, dz =0</math>
 <br> [[2014 Summer MA 598C Weigel|Back to 2014 Summer MA 598C Weigel]]
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