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A First Course in Complex Analysis: (Synthesis Lectures on Mathematics & Statistics)

(Paperback)

Allan R. Willms,

Springer International Publishing AG (Publisher)

Published

2022

Reviews

Mathematics and Science Mathematics

By: Allan R. Willms | Publisher: Springer International Publishing AG | Released: 19 Apr 2022

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This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.