Development of an Interactive Visualization Tool for Conformal Mappings in Complex Analysis

Abstract

This report summarizes the development of an interactive application designed to facilitate the teaching and learning of complex analysis through the visualization of conformal mappings. While conformal mappings are fundamental in the theory of complex functions, most standard textbooks provide only a limited number of illustrative figures, leaving a gap in visual resources for learners. The developed tool addresses this gap by enabling users to input complex functions and generate contour maps, thereby promoting intuitive understanding. A preliminary survey indicates that similar interactive services are scarce, particularly in Japanese-language contexts. Future work will focus on expanding the range of supported mappings, incorporating dynamic visualization features, and evaluating the educational impact through classroom implementation.