How do I show that the change of variable:
x = rcosθ , y = rsinθ
converts the Laplace equation uxx + uyy = 0 to
urr + 1/r ur + 1/r2 uθθ = 0
Here is my understanding:
uxx is the second partial derivative of u with respect to x, also written as d2u / d2x, but what is the equation with u in it that I have to differentiate?