- #1
randybryan
- 52
- 0
I've been given a function U(x,y) where f(z) = U(x,y) + iV(x,y)
and asked to check if it is harmonic and then work out what V(x,y) is
U(x,y) = [tex]\frac{y}{(1 - x)^{2} + y^{2}}[/tex]
To check if it is harmonic I can see if d2U/dx2 + d2U/dy2 = 0
I've tried differentiating and it's fairly arduous, so I'm thinking it might be easier to use polar co-ordinates (As a lot of the other questions simplify when doing this). Can anyone think of a suitable substitution to make the differentiation easier?
the answer in the back of the book says that f(z) = -i / (1 - z)
and asked to check if it is harmonic and then work out what V(x,y) is
U(x,y) = [tex]\frac{y}{(1 - x)^{2} + y^{2}}[/tex]
To check if it is harmonic I can see if d2U/dx2 + d2U/dy2 = 0
I've tried differentiating and it's fairly arduous, so I'm thinking it might be easier to use polar co-ordinates (As a lot of the other questions simplify when doing this). Can anyone think of a suitable substitution to make the differentiation easier?
the answer in the back of the book says that f(z) = -i / (1 - z)