A graduate course on complex analysis, equivalent to an incoming graduate student one-semester (or a bit more) class.
We state and prove Rouché's theorem which tells us that if holomorphic functions are close on a cycle they have the same number of zeros inside, alternatively with meromorphic functions, the difference between the number of zeros and poles is the same (subsection 5.4.2 in the book).
The course is based on the book "Guide to Cultivating Complex Analysis", which is available freely online at
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 An...
Негізгі бет 51. Rouché's theorem (Cultivating Complex Analysis 5.4.2)
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