Domain Coloring and the Argument Principle. Issue 8 (21st October 2017)

• Record Type: Journal Article
• Authors: Farris, Frank A.
• Is Part Of: PRIMUS. Volume 27:Issue 8/9(2017)
• Page Start: 827
• Page End: 844
• Publication Date: 2017-10-21
• Subjects: Complex variables -- Argument Principle -- domain coloring -- teaching -- contour integrals; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2016.1234526
• Languages: English
• ISSNs: 1051-1970

Abstract

Abstract: The domain-coloring algorithm allows us to visualize complex-valued functions on the plane in a single image—an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the Argument Principle, which relates the count of poles and zeros of a meromorphic function inside a contour to the accumulated change in argument of the function around the contour. Throughout, I offer connections to standard learning goals of courses in complex variables.