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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.

and complex functions f(z). One natural starting point is the d’Alembert solution formula of the one-dimensional wave equation — see [20] — which was based on the factorization = ∂2 t − c 2 ∂2 x= (∂t− c∂x)(∂t+ c∂x) of the linear wave operator. …

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