Complex Analysis: Theory and Applications · Problem 3.3.1

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · harmonic-functions-identification

Problem

Determine where the following functions are harmonic. (a)

u(x,y) = e^x \cos y

and

v(x,y) = e^x \sin y

. (b)

u(x,y) = \ln(x^2 + y^2)

for

(x,y) \neq (0,0)