51³ÉÈËÁÔÆæ

Course Description

Summary

Differential equations are the most powerful and most pervasive mathematical tool in the sciences and are fundamental in pure mathematics as well. Almost every system whose components interact continuously over time can be modeled by a differential equation, for example, planets, stars, fluids, electric circuits, predator and prey populations, epidemics, and economics. We will start by studying the classical theory of ordinary differential equations then we will develop dynamical systems approaches to understanding more complex and nonlinear systems. The goal throughout the course will be to better understand the behavior of each system or set of equations being studied through the use of the advanced mathematical techniques. A solid working understanding of derivatives and how to compute them will underly much of our work. Some familiarity with integration will also be required.