Explore the fascinating world of linear systems of differential equations in this 31-minute lecture from The Great Courses Plus. Delve into the practical applications of linear algebra, from search engine optimization to data recovery and budget maximization. Learn how to use matrix and vector notation, find equilibrium points, derive straight line solutions, and understand the linearity principle. Discover the power of phase plane visualization, explore linear independence among vectors, and uncover the relationship between homogeneous and non-homogeneous solutions. Gain insights into decaying exponentials through straight line solutions, all while decoding the mathematical intricacies of the universe with Dr. Robert L. Devaney as your guide.