Chaotic dynamical systems in the undergraduate curriculum
Bruce S. Elenbogen · International Journal of Mathematical Education in Science and Technology · 1990
The topics of dynamical systems, chaos and fractals have a growing importance in mathematics. This paper discusses an attempt at bringing a course in chaotic dynamical systems to the undergraduate level. The paper discusses the choices of source materials, topics, homework, and computer projects and makes recommendations based on experiences encountered in presenting such a course at the University of Michigan‐Dearborn. The last 25 years have seen a major increase in the interest in the study of nonlinear dynamical systems. The qualitative techniques discussed in this field have been applied to nonlinear problems ranging from physics and chemistry to economics and even art. Unlike the specific information generated in the solution of a differential equation, dynamical systems deal with the qualitative behaviour of all solutions of a system. The analysis involves techniques from a variety of mathematical sources and can serve to heighten a students’ appreciation of the beauty and unity of mathematics. The following is a discussion of a special topics course in chaotic dynamical systems at the University of Michigan‐Dearborn. The subject is not usually taught at the undergraduate level, but a course in chaotic dynamical systems can be a valuable addition to the undergraduate mathematics curriculum.