Some notes in my desk drawer
I have written notes on various topics over the years. So far, only one set of notes is self-contained enough and useful enough—and not ultimately incorporated in a paper—to make is here, but I hope for more.
This started with a set of notes I wrote while teaching the first quarter of graduate complex analysis, in which I proved a version of Cauchy's integral theorem using the divergence theorem. I kind of liked that approach, because using the divergence theorem requires one to relate real path integrals to complex path integrals, which are often left unmotivated. Not letting go, I decided to push it further to uncover some of the connections between complex analysis and incompressible fluid mechanics. There is nothing really new in this paper, with the possible exception of the theorem in the last section, which I have not seen in the literature, though it is almost certainly there somewhere. Some of what I wrote here made it into my 31st publication, which you can find here.
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