Explorations In Complex Analysis (classroom Resource Materials)

This book is written for mathematics students who have encountered basic complex analysis and want to explore more advanced project and/or research topics. It could be used as (a) a supplement for a standard undergraduate complex analysis course, allowing students in groups or as individuals to explore advanced topics, (b) a project resource for a senior capstone course for mathematics majors, (c) a guide for an advanced student or a small group of students to independently choose and explore an undergraduate research topic, or (d) a portal for the mathematically curious, a hands-on introduction to the beauties of complex analysis. 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. There are more than 15 Java applets that allow students to explore the research topics without the need for purchasing additional software. 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. "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."--[Source inconnue]