Let (r, θ) denote the usual polar coordinates. Show that if U(r, θ) is a harmonicfunction, then so is V (r, θ) = U(1/r, −θ).
Let (r, θ) denote the usual polar coordinates. Show that if U(r, θ) is a harmonicfunction, then so is V (r, θ) = U(1/r, −θ).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Let (r, θ) denote the usual polar coordinates. Show that if U(r, θ) is a harmonic
function, then so is V (r, θ) = U(1/r, −θ).
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