(Renection in a circle) Let r, 0 be polar coordinates. If

Chapter 12, Problem 12.10

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(Renection in a circle) Let r, 0 be polar coordinates. If lI(r. 0) satisfies V2 l/ = 0, show that the function v(r. 0) = lI(llr, 0) satisfies V2 v = O. What are l/ = r cos 0 and v in terms of x and y? Answer the same question for u = r2 cos 0 sin 0 and v.

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