A first-order differential equation whose right-hand-side does not explicitly depend on the independent variable is referred to as autonomous. In this lecture we focus on autonomous ODEs and present the method of phase line diagrams for analyzing them. Phase lines are a quick and easy way to geometically represent the behaviour of solutions to differential equations without having to solve it. They bare significant resemblance to slope/direction fields from the first lecture, but are often easier to sketch out. Phase line diagrams are illustrated with two examples coming from ecology.
This course is taught by Jason Bramburger for Concordia University.
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
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