APPLICATIONS OF DIFFERENTIAL CALCULUS TO ARCHITECTURE - Rivera, Edwin Rivera; Ramos, Patricia Mattei; Hernández, Franchesca M. Carrasquillo; Hernández, Nydiaam Vilanova (International Journal of Research -GRANTHAALAYAH, 2025)
Differential calculus constitutes a fundamental mathematical tool in contemporary architectural design and analysis. This documentary research examines the practical applications of differential calculus in architecture, demonstrating how abstract mathematical concepts transform into tangible constructive solutions. The study analyzes the application of mathematical limits to establish design restrictions, guarantee structural safety, and optimize the behavior of high-rise buildings and complex geometries. Derivatives emerge as crucial analytical instruments for calculating curvatures, optimizing organic structures, and analyzing energy efficiency in emblematic works such as the Guggenheim Museum Bilbao. Differential geometry enables the modeling of complex surfaces and non-Euclidean spaces, while integrals facilitate the quantification of geometric properties, structural load analysis, and optimization of thermal behavior in sustainable buildings. The document also explores advanced applications such as multiple integrals, Gaussian series, partial derivatives, and Lebesgue measure theory, evidencing their relevance in parametric design and computational architecture. The results demonstrate that mastery of differential calculus not only improves the technical precision of architectural design but also expands the frontiers of creativity, enabling architects to create habitable, safe, and aesthetically innovative spaces that respond with scientific rigor to contemporary social and environmental needs.