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

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 related lectures from this and other courses here: https://www.youtube.com/playlist?list=PL4d5ZtfQonW0fTwPsRvvg9hMJllVyj1l3 You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.