Linear Planar Systems - Dynamical Systems | Lecture 14

Now that we have thoroughly discussed one-dimensional dynamical systems, we turn to those that are two-dimensional. In this lecture we provide the basics of linear planar dynamical systems. It is demonstrated that much of their analysis comes down to identifying eigenvalues and eigenvectors. We focus much of our attention on sketching the phase planes for these linear dynamical systems as these sketches will become important in a few lectures for understanding nonlinear systems as well. For an application of planar linear systems, see my video on modelling Romeo and Juliette's love dynamics: https://www.youtube.com/watch?v=aQXLFXA-twI Related lectures from previous course on Ordinary Differential Equations: - Complex eigenvalues and oscillations: https://www.youtube.com/watch?v=ur2xT-Cj8fs&feature=youtu.be - Repeated eigenvalues and reduction of order: https://www.youtube.com/watch?v=eJks60DFOKw&feature=youtu.be 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.