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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.

The driving force behind many of the applications of complex analysis is the remarkable connection between complex functions and harmonic functions of two variables, a.k.a. solu-tions of the planar Laplace equation. To wit, the real and imaginary parts of any complex analytic function are automatically harmonic.

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