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A First Course in Complex Analysis
Hardcover
Series: Synthesis Lectures on Mathematics and Statistics
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ISBN13: 9781636393162
Publisher: Morgan & Claypool
Published: Apr 20 2022
Pages: 237
Language: English
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.
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