Series Solutions Near an Ordinary Point - Ordinary Differential Equations | Lecture 26 скачать в хорошем качестве

Series Solutions Near an Ordinary Point - Ordinary Differential Equations | Lecture 26

In the previous two video lectures we have applied the method of using power series to solve ODEs. The question is: can we just solve every ODE like this? In this lecture we focus on answering this question. We identify specific characteristics of an ODE to determine whether or not a series solutions exists and what its radius of convergence is. We introduce the notion of an analytic function - functions that are infinitely differentiable and have convergent power series about a given power. We further demonstrate that not every function that is infinitely differentiable has a power series. 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.