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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.

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 ...

  Analysis, Complex, Conformal, Complex analysis

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