Chapter 10 Applications of Harmonic Functions
A wide variety of problems in engineering and physics involve harmonic functions, which are the real or imaginary part of an analytic function. The standard applications are two dimensional steady state temperatures, electrostatics, fluid flow and complex potentials. The techniques of conformal mapping and integral representation can be used to construct a harmonic function with prescribed boundary values. Noteworthy methods include Poisson’s integral formulae; the Joukowski transformation; and Schwarz-Christoffel transformation. Modern computer software is capable of implementing these complex analysis methods.
