Course: CAAM 28200=STAT 28200
Title: Dynamical Systems with Applications
Instructor(s): Mary Silber
Class Schedule: Sec 01: TR 11:00 AM–12:20 PM in Pick Hall 022
Textbook(s): Strogatz, Nonlinear Dynamics and Chaos (any edition)
Prerequisite(s): Multivariable calculus (MATH 19520, 20000 or 20400, or PHYS 22100, or equivalent). Linear algebra, including eigenvalues and eigenvectors (MATH 19620 or STAT 24300, or equivalent). Previous knowledge of elementary differential equations is helpful but not required.
Description: This course is concerned with the analysis of nonlinear dynamical systems arising in the context of mathematical modeling. The focus is on qualitative analysis of solutions as trajectories in phase space, including the role of invariant manifolds as organizers of behavior. Local and global bifurcations, which occur as system parameters change, will be highlighted, along with other dimension reduction methods that arise when there is a natural time-scale separation. Concepts of bi-stability, spontaneous oscillations, and chaotic dynamics will be explored through investigation of conceptual mathematical models arising in the physical and biological sciences.