Abstract:

This work presents the design, implementation, and preliminary outcomes of an innovative course on complex variables, developed within an Advanced Mathematics subject for third-semester engineering students. The course was deployed through the Canvas learning management system and structured around active learning, flipped classroom dynamics, and problem-based methodologies. Its components included self-study materials, weekly agendas, quizzes, interactive videos, and diagnostic–formative–summative evaluations (EDAS).

A distinctive feature of the course was the integration of technological tools to foster visual and conceptual understanding of complex functions. Students worked with GeoGebra applets to explore line integrals, Taylor and Laurent series, vector fields, level curves of real and imaginary parts of complex functions, and Fourier transforms. Complementary Python-based applications allowed for the interactive study of complex integration, residues method, and improper integrals of rational functions. Visual activities using Matlab and Mathematica further supported the analysis of mappings in the complex plane through three-dimensional representations.

Preliminary results indicate improved conceptual performance and increased student autonomy in the use of mathematical tools. The course offers a replicable model for incorporating interactive technologies into higher mathematics education, with strong potential for enhancing both engagement and mathematical reasoning.

Keywords:

Higher Education, Complex Calculus, Geogebra, Mathematica.