Explorations In Complex Analysis (classroom Resource Materials)

A guide to help undergraduate students who have studied some complex analysis and want to explore additional topics in the field. It focuses on discovery, self-driven investigation, and creative problem posing.;Complex dynamics: chaos, fractals, the Mandelbrot set, and more / Richard L. Stankewitz and James S. Rolf -- Soap films, differential geometry, and minimal surfaces / Michael J. Dorf and James S. Rolf -- Applications to flow problems / Michael Brilleslyper, James S. Rolf -- Anamorphosis, mapping problems, and harmonic univalent functions / Michael J. Dorff, James S. Rolf -- Mappings to polygonal domains / Jane McDougall and Lisbeth Schaubroeck, James S. Rolf -- Circle packing / Ken Stephenson -- Background -- The Riemann sphere. Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.