This Department is dedicated to the application of mathematics in different fields of science. Differential equations are used as a common language and special emphasis is placed on the study of nonlinear problems.

The main lines of investigation address nonlinear phenomena described by differential equations and nonlinear dynamical systems in finite and infinite dimensions, using analytical, topological, asymptotic and numerical techniques. These areas of research cover very diverse applications including the following: the mechanics of solids and fluids, nonlinear optics, composite materials, quantitative aspects of biology, propagation of waves, coherent structures with nonlinear diffusion and solitons. In addition, recent work has also been carried out on mathematics and pre-hispanic land surveying.

This Department has a computer laboratory used by researchers and students, and has developed a hybrid cluster of computers working in parallel and contains GPU servers with 1800 processors.

From its beginnings, the Department has demonstrated a vocation for a horizontal approach to science, leading it to develop the University Project on Nonlinear Phenomena and Mechanics (FENOMEC by its acronym in Spanish; see www.fenomec.unam.mx), which operates as a “center without walls”. At this time, FENOMEC has 32 participating members from 10 different UNAM Departments, including all of the members from this Department.