Complex Analysis and Conformal Mapping
Complex Analysis and Conformal Mappingby Peter J. OlverUniversity of MinnesotaContents1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. Complex Functions. . . . . . . . . . . . . . . . . . . . . . . . . 2Examples of Complex Functions . . . . . . . . . . . . . . . . . . . 53. Complex Differentiation. . . . . . . . . . . . . . . . . . . . . . . 9Power Series and Analyticity . . . . . . . . . . . . . . . . . . . . 124. Harmonic Functions. . . . . . . . . . . . . . . . . . . . . . . . . 15Applications to Fluid Mechanics . . . . . . . . . . . . . . . . . . . 205. Conformal Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 27Analytic Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Conformality.
Conformal mappings can be effectively used for constructing solutions to the Laplace equation on complicated planar domains that are used in fluid mechanics, aerodynamics, thermomechanics, electrostatics, elasticity, and elsewhere. We assume the reader is familiar with the basics of complex numbers and complex arith-
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