- #1
TheCanadian
- 367
- 13
I am trying to find a harmonic function based on the conditions imposed in the images. I see how one can make an Ansatz that ## \phi(x,y) = xy + \psi(x,y)## and can arrive at the solution given by ensuring the function satisfies the given conditions. But is there a more systematic method to solving these types of questions? In the hint, it says to use ##z^2## and it may be clear that ##z^2 = x^2 + y^2 + 2ixy##, and that the imaginary part recovers a form similar to the boundary conditions, but is there something more general one can do with this hint?
Any suggestions on how to approach problems of this sort?
Any suggestions on how to approach problems of this sort?