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Complex Analysis and Conformal Mapping

Complex Analysis and Conformal Mappingby Peter J. OlverUniversity of MinnesotaContents1. Introduction.. 22. Complex Functions.. 2 Examples of Complex Functions .. 53. Complex Differentiation.. 9 Power Series and Analyticity .. 124. Harmonic Functions.. 15 Applications to Fluid Mechanics .. 205. Conformal Mapping .. 27 Analytic Maps .. 27 Conformality .. 33 Composition and the Riemann Mapping Theorem .. 38 Annular Domains .. 426. Applications of Conformal Mapping .. 44 Applications to Harmonic Functions and Laplace s Equation.. 44 Applications to Fluid Flow .. 48 Poisson s Equation and the Green s Function.

The term “complex analysis” refers to the calculus of complex-valued functions f(z) depending on a single complex variable z. To the novice, it may seem that this subject should merely be a simple reworking of standard real variable theory that you learned in first year calculus. However, this na¨ıve first impression could not be ...

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