2025 ASEE Annual Conference & Exposition

In Spring of 2024, our institution offered a math course called ‘Dynamical Systems and Chaos’, which served as an elective course for engineering and applied mathematics students. The purpose was to introduce students to the analysis of long-term behaviors and stability in nonlinear dynamical systems, which have applications in modeling real-world problems. Faculty used active learning pedagogy in the classroom and made regular adjustments to center student discussion and questions. Beyond homework and exams, students completed a challenge project centered on mathematical modeling with differential equations.

Topics for this course followed a typical introductory syllabus on nonlinear dynamics, focusing on equilibrium solutions and limit cycles in systems of first-order differential equations, along with stability and bifurcation analysis. Classic examples of chaos in continuous systems and discrete maps were also explored. The course included an additional learning outcome targeted at relevant applications of dynamical systems. Since mathematical modeling is foundational to both engineering and applied mathematics, this aspect of the course could be developed further towards student interests. Student and faculty feedback on the course was generally positive but mentioned some conceptual and computational difficulties with the material.

It was important to reflect on the initial offering of this course in the context of our engineering and applied mathematics programs. Given our institution's focus on career preparation and real-world problem solving, future offerings present an opportunity to develop students’ interest and better meet their needs. In this paper, we will give details about the course and student feedback. Possible curricular and pedagogical changes will also be discussed.