Math 391 Lecture 10 - The Wronskian and what it tells us about solutions to SOLDEs

In this lecture we explore the Wronskain. We motivate its definition and show how it can determine whether two solutions form a fundamental set of solutions to a second order linear differential equation (SOLDE), and in what context it guarantees the existence of a unique solution. We also prove Abel's theorem--a theorem that determines, up to a multiplicative constant, the value of the Wronksian without knowing what the fundamental solutions are.

[phillipfry]

Thank you for posting these. They have been my only substitute for this class and I am passing because of you.

[teebiz]

just three minutes in the lecture video and i find the right approach - downloaded it will go through it .... thanks

[pipertripp]

Great lecture. I'm teaching myself ODEs using Boyce and DiPrima and this lecture was great commentary on section 3.2. I really enjoyed it! Thanks for putting it out there.

[UnforsakenXII]

Quick question, is it advisable to study introductory Linear Algebra alongside this or will it have nothing to do with this class? Just wondering because a few people said it was better to do LA before DE. (Or should I just do LA once I hit 392?)