Differential Equations 1: Higher order ordinary differential equations - theory & practice lecture 1

From Oxford Mathematics

In the first of two lectures from Philip Maini's Differential Equations 1 second year course, we extend Picard's Theorem on the existence and uniqueness of solutions for a first order ordinary differential equation (ODE) to higher order and coupled systems of ODEs. Then we focus on plane autonomous systems and begin to develop methods for analysing the behaviour of solutions through identifying critical points, carrying out linear stability analysis and plotting phase planes. You can watch re...