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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.. 73 The Calculus of Residues .. 75 Evaluation of Real Integrals .. 80 References.. 861/7/221c 2022 Peter J.

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 …

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