Complex Roots and Oscillations - Ordinary Differential Equations | Lecture 14 скачать в хорошем качестве

Complex Roots and Oscillations - Ordinary Differential Equations | Lecture 14

In this lecture we return to discussing the characteristic equation from Lecture 12. We now focus on the case of complex roots. In this case we can use Euler's formula to convert the complex solutions to the ODE to real-valued solutions that include an oscillatory component. Examples are provided to illustrate the theory, while we also use the Wronskian to demonstrate that we have indeed identified a fundamental set of solutions to the second order differential equation. 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.