Taylor & Francis
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.
Farris, F. A. (2017). Domain Coloring and the Argument Principle. PRIMUS, 27(8–9), 827–844. https://doi.org/10.1080/10511970.2016.1234526