This is a lecture recorded by Prof. Steven Strogatz for his undergraduate class on "Applied Complex Analysis" at Cornell University. In this lecture, Prof. Strogatz walks the students through a magnificent proof of one of the main results of complex analysis, known as Cauchy's theorem. (It's also sometimes called Cauchy's integral theorem, or the Cauchy-Goursat theorem, since the proof shown here is due to Goursat.)

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