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## Main Question or Discussion Point

In

the earlier homework included something like u = xy, show it's harmonic. EASY as pi. But I'm not really sure how to set this problem up. I understand the concept that a harmonic function will look like [tex] \nabla^{2} u = 0 [/tex], but I'm not sure how to find all polys of degree 2.

I started out doing something like

[tex] u = a_{2}x^{2}_{1} + a_{1}x_{1} + a_{0} + b_{2}x^{2}_{2} + b_{1}x_{2} + b_{0}+... [/tex]

and taking the partial with respect to each x

Any suggestions?

**R**, I am to find all homog. polys (deg 2) that are harmonic.^{2}the earlier homework included something like u = xy, show it's harmonic. EASY as pi. But I'm not really sure how to set this problem up. I understand the concept that a harmonic function will look like [tex] \nabla^{2} u = 0 [/tex], but I'm not sure how to find all polys of degree 2.

I started out doing something like

[tex] u = a_{2}x^{2}_{1} + a_{1}x_{1} + a_{0} + b_{2}x^{2}_{2} + b_{1}x_{2} + b_{0}+... [/tex]

and taking the partial with respect to each x

_{i}but that's not getting me very far.Any suggestions?