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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.

are based on Euler’s formula, and are of immense importance for solving differential equa-tions and in Fourier analysis. Further examples will appear shortly. There are several ways to motivate the link between harmonic functions u(x,y), meaning solutions of the two-dimensional Laplace equation ∆u= ∂2u ∂x2 + ∂2u ∂y2 = 0, (2.3)

  Mapping, Equations, Conformal, Euler, Conformal mapping

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