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 . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Composition and the Riemann Mapping Theorem . . . . . . . . . . . 37Annular Domains . . . . . . . . . . . . . . . . . . . . . . . . . 416. applications of Conformal Mapping .
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.
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