Complex analysis: Harmonic functions

Описание к видео Complex analysis: Harmonic functions

This lecture is part of an online undergraduate course on complex analysis.

We study the question: when is a function u the real part of a holomorphic function w=u+iv? An easy necessary condition is that u mist be harmonic. We use the Caucy-Riemann equations to show that this condition is also sufficient if u is defined in a simply connected open set, and given an example to show that it need not be sufficient if u is defined on a non-simply connected set. So on simply connected open sets harmonic functions are the same as the real parts of holomorphic functions.

For the other lectures in the course see    • Complex analysis  

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