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 . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Conformality.

rational functions, exponentials, trigonometric functions, logarithms, and many more — have natural complex extensions. For example, complex polynomials p(z) = anzn+ a n−1 z n−1 + ···+ a 1 z+a0 (2.2) are complex linearcombinations (meaning thatthe coefficients akareallowed tobe complex numbers) of the basic monomial functions zk= (x+ ...

  Mapping, Functions, Conformal, Trigonometric, Trigonometric functions, Conformal mapping