A graduate course on complex analysis, equivalent to an incoming graduate student one-semester (or a bit more) class.

We prove the Harnack's inequality in the disc and the general version in an arbitrary domain. With the inequality we prove Harnack's principle on convergence of harmonic functions. (Subsections 7.2.3 and 7.2.4 in the book).

The course is based on the book "Guide to Cultivating Complex Analysis", which is available freely online at

https://www.jirka.org/ca/

(You can also buy an inexpensive paperback copy, the best way to support this project)

See the course playlist:    • Cultivating Complex Analysis