Complex Analysis: Lecture 10: harmonic functions

here we study the connection between holomorphic complex functions and harmonic functions on the plane. We find the each complex differentiable function on a domain (holomorphic) there is a pair of harmonic functions. Such a pair is formed by u and its harmonic conjugate v. The problem of finding the harmonic conjugate is an exercise in partial integration much like the problem of finding a potential energy function for a conservative vector field in multivariate calculus. Finally, we study the geometry of the level curves of the u and v constant curves for a holomorphic f=u+iv. Conformality is shown and demonstrated (sorry for the rush at the end, the notes are clear even if I'm not here)

[georgesadler]

Professor Cook, thank you for another incredible lecture on harmonic functions.

[ComputerNerd]

at 10:00 i think you meant x*sin(1/x) not (x^2)sin(1/x) because (x^2)sin(1/x) has a continuous derivative.

[GodsLittlegizmoguy]

Thank you for keeping God in school. Where God is allowed to remain, His blessings are sure to follow!

[willgoodwin]

WTF are you doing saying prayers before class, that is extremely weird dude. Please stop, for the good of the children.