MAXIMUM PRINCIPLE -- Part 1 -- Core Theorems of Complex Analysis

If you're interested in personal help, I've posted my tutoring services on Fiverr: https://www.fiverr.com/s/dDYkBlz I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to do some online tutoring. Part 2: https://www.youtube.com/watch?v=jmP4VlgZvb0 Part 3: https://www.youtube.com/watch?v=fLnRDhhzWKQ In this video, we give a proof of the Maximum Principle, which is a monumental result in the subject of complex analysis. The maximum principle is also referred to as the maximum modulus principle, and states that the modulus of a holomorphic function cannot achieve an interior maximum. The proof we give here is elementary, albeit requiring the less-elementary open mapping theorem, and is due to the late Professor Alexander Isaev. 👍 To support the channel, hit the like button and subscribe. 🐸 To learn how I make these animations using Grant Sanderson's (3Blue1Brown) program Manim, check out my quick intro to Manim on Skillshare: https://www.skillshare.com/r/profile/Kyle-B/344454857 Source code for this video: https://github.com/Kylebroder/ManimCode/blob/main/Schwarz.py 🎸 Music in this video is from Epidemic Sound: https://www.epidemicsound.com/referral/yi0wzw/ Ways to support the channel: 🏆 Support the channel over on Patreon https://www.patreon.com/KyleBroder 🐸 Support the channel by signing up to a free trial of Skillshare using the link https://www.skillshare.com/r/profile/Kyle-B/344454857 FYI, these are affiliate links 💪🙏 These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University.