By Bruce P. Palka
This ebook offers a rigorous but common advent to the idea of analytic services of a unmarried complicated variable. whereas presupposing in its readership a level of mathematical adulthood, it insists on no formal necessities past a valid wisdom of calculus. ranging from simple definitions, the textual content slowly and punctiliously develops the information of advanced research to the purpose the place such landmarks of the topic as Cauchy's theorem, the Riemann mapping theorem, and the theory of Mittag-Leffler will be handled with out sidestepping any problems with rigor. The emphasis all through is a geometrical one, such a lot suggested within the wide bankruptcy facing conformal mapping, which quantities basically to a "short path" in that very important zone of complicated functionality conception. every one bankruptcy concludes with a big variety of routines, starting from uncomplicated computations to difficulties of a extra conceptual and thought-provoking nature.
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