Toronto Math Forum
MAT3342018F => MAT334Lectures & Home Assignments => Topic started 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 $u(x,y)=\text{Re}(f)$?

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.