20.1 Complex Functions as Mappings

20.2 Conformal Mappings

20.3 Linear Fractional Transformations

20.4 Schwarz–Christoffel Transformations

20.5 Poisson Integral Formulas

20.6 Applications

Chapter 20 in Review

In earlier chapters we used Fourier series and integral transforms to solve boundary-value problems involving Laplace’s equation. Conformal mapping methods discussed in this chapter can be used to transfer known solutions of Laplace’s equation from one region to another. In addition, fluid flows around obstacles and through channels can be determined using conformal mappings.