Faculty of Khan | Bessel Functions and the Frobenius Method @FacultyofKhan | Uploaded 7 years ago | Updated 7 minutes ago
This video is a continuation to my Intro to Frobenius Method lecture. It's part 4 of my 'Topics in ODEs' playlist. In this video, I discuss the types of solutions to an ODE solved by the Frobenius Method which depend on the nature of the roots to the indicial equation. I then solve Bessel's equation by the Frobenius method.
Questions? Ask me in the comments!
Errata: The second term in the second solution for the repeated roots in the Frobenius Method (starts at 3:15) should begin at n = 1, and not n = 0. Also, the ln(x)'s in the y2's of both the repeated roots and integer different roots should be ln|x-x0|. In many examples, x0 = 0 anyway, so we should be fine. They're small mistakes, so hopefully it shouldn't be too impactful.
Prereqs: The first 3 videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9ATVsK2Q84ghjBgIk5faHNc
Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMUHNIN3FodXVIUEE/view?usp=sharing&resourcekey=0-QJZq5u6sxm6P42JI_woWIA
Support me if you feel like it at Patreon: patreon.com/user?u=4354534
This video is a continuation to my Intro to Frobenius Method lecture. It's part 4 of my 'Topics in ODEs' playlist. In this video, I discuss the types of solutions to an ODE solved by the Frobenius Method which depend on the nature of the roots to the indicial equation. I then solve Bessel's equation by the Frobenius method.
Questions? Ask me in the comments!
Errata: The second term in the second solution for the repeated roots in the Frobenius Method (starts at 3:15) should begin at n = 1, and not n = 0. Also, the ln(x)'s in the y2's of both the repeated roots and integer different roots should be ln|x-x0|. In many examples, x0 = 0 anyway, so we should be fine. They're small mistakes, so hopefully it shouldn't be too impactful.
Prereqs: The first 3 videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9ATVsK2Q84ghjBgIk5faHNc
Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMUHNIN3FodXVIUEE/view?usp=sharing&resourcekey=0-QJZq5u6sxm6P42JI_woWIA
Support me if you feel like it at Patreon: patreon.com/user?u=4354534
