Problem 3 (20 points) Let u(T,θ) = e^f sin θ. Verify that the given function is harmonic on the whole xy-plane. b) Find the harmonic conjugate of u.
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a) To verify that the given function is harmonic, we need to show that it satisfies Laplace's equation: ∇²u = 1/r ∂/∂r (r ∂u/∂r) + 1/r² ∂²u/∂θ² = 0 where r and θ are the polar coordinates. Show more…
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