Complex Analysis and Conformal Mapping
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.
useful consequences stems from the elementary observation that the composition of two complex functions is also a complex function. We re-interpret this operation as a complex change of variables, producing a conformal mapping that preserves (signed) angles in the Euclidean plane. Conformal mappings can be effectively used for constructing ...
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