In the previous set of notes we saw that functions that were holomorphic on an open set enjoyed a large number of useful properties, particularly if the domain was simply connected. 11,793 more words

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#### Math 246A, Notes 3: Cauchy's theorem and its consequences

We now come to perhaps the most central theorem in complex analysis (save possibly for the fundamental theorem of calculus), namely Cauchy’s theorem, which allows one to compute (or at least transform) a large number of contour integrals even without knowing any explicit antiderivative of . 10,288 more words