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About this book
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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Table of contents (8 chapters)
Authors and Affiliations
About the author
Allan R. Willms is a professor in the Department of Mathematics & Statistics at the University of Guelph in Canada. He earned a B.Math. (1992) and an M.Math. (1993) from the University of Waterloo in Canada and received a Ph.D. (1997) from Cornell University in Ithaca, NY, USA. He spent five years as a faculty member in the Department of Mathematics & Statistics at the University of Canterbury in Christchurch, New Zealand, after which he moved to Guelph in 2003. He is a generalist applied mathematician and says of himself “I know a little about a lot of things but not much about anything.” His research has included neuronal ion channels, antibiotic resistance, Cheyne-Stokes respiration, resonant Hopf bifurcations, Huygens’ clocks, climate change, cat bladder measurements, parameter range reduction for ODE models, fish population dynamics, E. coli contamination in beef processing plants, epidemiology, robot path planning, cytokine storms, and pathogen survival in manure.
Bibliographic Information
Book Title: A First Course in Complex Analysis
Authors: Allan R. Willms
Series Title: Synthesis Lectures on Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-031-79176-5
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 11
Copyright Information: Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-79171-0Published: 19 April 2022
eBook ISBN: 978-3-031-79176-5Published: 06 June 2022
Series ISSN: 1938-1743
Series E-ISSN: 1938-1751
Edition Number: 1
Number of Pages: XIX, 217
Topics: Mathematics, general