A First Course in Complex Analysis

Know about the book -

A First Course in Complex Analysis is written by Allan R. Willms and published by Springer Nature. It's available with International Standard Book Number or ISBN identification 3031791762 (ISBN 10) and 9783031791765 (ISBN 13).

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.