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 . . . . . . . . . . . 38Annular Domains.
1/7/22 5 c 2022 Peter J. Olver. Figure 2. Real and Imaginary Parts of ez. of complex polynomials provide a large variety of harmonic functions. The simplest case is 1 z = x x2 + y2 − i y x2 + y2, (2.11) whose real and imaginary parts are graphed in Figure 1. Note that these functions have
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