Complex Analysis: Theory and Applications · Problem 3.3.4

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · harmonic-arctan

Problem

Let

v(x,y) = \arctan\left(\dfrac{y}{x}\right)

for

x \neq 0

. Compute the partial derivatives of

v

and verify that

v

satisfies Laplace's equation.