History and Preliminaries - Dynamical Systems | Lecture 1

I begin this lecture series by taking you through the history of dynamical systems, tracing the evolution of the field from Newton to Poincaré and into the developments of the twentieth century. Along the way, I introduce key preliminaries to formalize the notation and define the types of systems we will study. We explore autonomous systems of equations and discuss the crucial role of nonlinearity in shaping system behaviour. Finally, I highlight the challenges and frontiers of high-dimensional systems, setting the stage for the deeper explorations that will follow in the series. This lecture combines historical context, foundational theory, and a glimpse of the cutting-edge questions driving research in dynamical systems today. 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.