Answers to quiz 6

1. The Laplace equation fxx + fyy = 0 in polar coordinates x = r cosθ, y = r sinθ is frr + fr/r + fθθ/r2 = 0 (Eq. 11.19)
2. If f(x,y) satisfies fxy = 0 then by integration with respect to y we observe that fx is a function φ of x only, and by subsequent integration with respect to x, f is the integral of φ(x) plus an arbitrary function of y: f = g(x) + h(y), g, h are arbitrary functions.
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