Harmonic function

• May 27th 2009, 11:33 AM
NaNa
Harmonic function
(a)Show that the function u=x^2+y is not a harmonic function.
(b)show the function v=x+2y is part of harmonic conjugate and say what f(z) is.

Any help?!?!:/
• May 27th 2009, 11:40 AM
Moo
Quote:

Originally Posted by NaNa
(a)Show that the function u=x^2+y is not a harmonic function.

$\frac{\partial^2u}{\partial x^2}=2$
$\frac{\partial^2u}{\partial y^2}=0$

Is $\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}$ equal to 0 ?

Any thought you've given to your problems ?!?!
• May 27th 2009, 11:44 AM
NaNa
is not (du)^2/(dx)^2+(dv)^2/(dy)^2?!?!
• May 27th 2009, 11:54 AM
NaNa
in the next one that I have to do is this:
v=x+2y
dv/dx=1
du/dx=dv/dx so u=x+f(y)
dv/dy=2
du/dy=dv/dy so u=2y+f(x)

So v=x+2y
f(z)=x+2y+i(x+2y)