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.

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. …

  Mapping, Functions, Waves, Conformal, Conformal mapping