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Complex Analysis and Conformal Mapping

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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 . . . . . . . . . . . 38Annular Domains.

Complex analysis is the culmination of a deep and far-ranging study of the funda- mental notions of complex differentiation and integration, and has an …

  Analysis, Mapping, Conformal, Conformal mapping

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