A First Course in Complex Analysis

Allan R. Willms (Autor)

Buch | Softcover

XIX, 217 Seiten

2022
Springer International Publishing (Verlag)
978-3-031-79171-0 (ISBN)

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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.

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.

Preface.- Acknowledgments.- Basics of Complex Numbers.- Functions of a Complex Variable.- Differentiation.- Contour Integration.- Cauchy Theory.- Series.- Residues.- Conformal Mapping.- Author's Biography.- Index.

Erscheinungsdatum	06.06.2022
Reihe/Serie	Synthesis Lectures on Mathematics & Statistics
Zusatzinfo	XIX, 217 p.
Verlagsort	Cham
Sprache	englisch
Maße	191 x 235 mm
Gewicht	460 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	3-031-79171-1 / 3031791711
ISBN-13	978-3-031-79171-0 / 9783031791710
Zustand	Neuware