https://tube.cosmicflow.space/videos/watch/93cd4cfc-ba0b-4ee6-b2f2-0a9d81d7bd01 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 https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN Sat, 10 Oct 2026 19:12:28 GMT https://validator.w3.org/feed/docs/rss2.html PeerTube - https://tube.cosmicflow.space https://tube.cosmicflow.space/lazy-static/avatars/8891227d-e60f-40aa-88be-4c856c6a73dc.png https://tube.cosmicflow.space/videos/watch/93cd4cfc-ba0b-4ee6-b2f2-0a9d81d7bd01 All rights reserved, unless otherwise specified in the terms specified at https://tube.cosmicflow.space/about and potential licenses granted by each content's rightholder.