51³ÉÈËÁÔÆæ

Course Description

Summary

Dynamical systems are interactions that change in somewhat predictable ways. For these systems, rules can be written to describe the future state of a system from knowledge of present and past states. These rules are used to model a wide variety of phenomena in the physical, biological, social and economic sciences. This course will build on calculus skills and visual intuition to understand complex interactions in physical systems. It will be an introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry. Emphasis will be placed on using analytical methods, concrete examples, and geometric thinking. Topics will include one-dimensional systems; bifurcations; phase plane analysis; nonlinear oscillators; and Lorenz equations, chaos, strange attractors, fractals, iterated mappings, period doubling, renormalization.