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We seek to understand how dynamical systems evolve, how that evolution depends on the various parameters of the system, and how we might manipulate those parameters to optimize an outcome. We will explore the language of dynamics by deepening our understanding of differential and difference equations, study parameter dependence and bifurcations, and explore optimal control through Pontryagin’s maximum principle and Hamilton-Jacobi-Bellman equations. These tools have broad application in ecology, economics, finance, and engineering, and we will draw on basic models from these fields to motivate our study.
Grading: yes pass/fail option,
yes fifth course option
exams and homework assignments
MATH 209 or PHYS 210, and MATH 350 or 351, or permission of the instructor
Preference will be given to senior math majors.
This is a 400 level math course.