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Complex Analysis and Conformal Mapping

Complex Analysis and Conformal Mappingby Peter J. OlverUniversity of MinnesotaContents1. Introduction.. 22. Complex Functions.. 2 Examples of Complex Functions .. 53. Complex Differentiation.. 9 Power Series and Analyticity .. 124. Harmonic Functions.. 15 Applications to Fluid Mechanics .. 205. Conformal Mapping .. 27 Analytic Maps .. 27 Conformality .. 33 Composition and the Riemann Mapping Theorem .. 38 Annular Domains .. 426. Applications of Conformal Mapping .. 44 Applications to Harmonic Functions and Laplace s Equation.. 44 Applications to Fluid Flow .. 48 Poisson s Equation and the Green s Function ..537. Complex Integration.. 56 Cauchy s Theorem .. 61 Circulation and Lift .. 65 Cauchy s Integral Formula .. 71 Derivatives by Integration .. 72 Liouville s Theorem and the Fundamental Theorem of Algebra.

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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  Mapping, Conformal, Conformal mapping

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