In this lecture we begin trying to understand how solutions to dynamical systems evolve in time. We begin by restricting ourselves to differential equations of a single dependent variable, so-called scalar systems. In this case we can sketch out phase line diagrams that fully capture the dynamics of the problem. This lecture provides the basics of sketching phase line diagrams and shows how to interpret them to answer problems in dynamical systems.
For the derivation of the water tank differential equation, see this lecture: https://www.youtube.com/watch?v=hGJUFUfu9mA
This course is taught by Jason Bramburger for Concordia University.
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
Follow @jbramburger7 on Twitter for updates.