First Course in Complex Analysis

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.