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MAT334-2018F => MAT334--Lectures & Home Assignments => Topic started by: Min Gyu Woo on October 16, 2018, 08:32:30 PM

Title: Chapter 2.1 PG 80
Post by: Min Gyu Woo on October 16, 2018, 08:32:30 PM
There's this little portion of text before the defining Laplace's Equation that I am confused about.

It reads:

"A word of warning is merited here: Not every function $u(x,y)$ is the real part of an analytic function".

If we always define $f = u +iv$, doesn't this guarentee that $u(x,y)=\text{Re}(f)$?
Title: Re: Chapter 2.1 PG 80
Post by: Meiqun Lu on October 17, 2018, 06:42:40 PM
I think what the textbook is trying to say is that even though you could find a function f(z) whose real part can be written as u(x,y), but f(z) does not have to be analytic.