Green's Theorem: Calculus 3 Lecture 15.5

Green's Theorem: Calculus 3 Lecture 15.5: An explanation of Green's Theorem and how to apply it for Line Integrals of Simple Closed Curves on Non-Conservative Vector Fields.

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19:34 What is also seriously cool about this is that the conservative property of vector fields appears to be analogous to holomorphy of functions in complex analysis. Cauchy’s integral theorem states that the line integral of a holomorphic function taken along a simple closed curve inside a domain in the complex plane is zero. To show this, one uses Green’s theorem and demonstrates that the double integral evaluates to zero if the function is holomorphic. Hence, holomorphy in the complex plane creates an environment identical to conservation in vector fields. I never realised this - thank you very much, Professor Leonard!

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