Complex Analysis and Conformal Mapping
tions and in Fourier analysis. Further examples will appear shortly. There are several ways to motivate the link between harmonic functions u(x,y), meaning solutions of the two-dimensional Laplace equation ∆u= ∂2u ∂x2 + ∂2u ∂y2 = 0, (2.3) and complex functions f(z). One natural starting point is the d’Alembert solution formula
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