Introduction to the Frobenius Method

In this video, I introduce the Frobenius Method to solving ODEs and do a short example.

Questions? Ask them below!

Prerequisites: Regular series solutions of ODEs (basically those two series videos I made).

Also, one of the comments pointed out that I made a mistake at 8:45: when you plug r1=1 into the coefficient of the a1 term, you get 3! For r2=0.5 you get 1. Still, that doesn't change the fact that plugging these values of r into the other terms will give us non-zero coefficients for the a1, a2, a3, etc.

[nishadingale]

your knowledge of mathematical methods is good; but your sense of humor is the best!

[lilpandaftw]

This is a great video! I appreciate that you explain seemingly simple ideas, just in case students are lost. You're awesome!

[kadekevin]

this is a family show? yeah, my 8 year old niece is interested in how frobenius differs from bessel

I really appreciate you taking the time to make that comment at 11:00

[eamonnsiocain]

I liked the pace of this video. When I needed to double-check, I simply paused the video -- which is far easier than trying to skip ahead when the pace is too slow.

[EngelUniverse]

This is an amazing explanation.
But for me:
First time I heard it: could not follow or get it at all!
then, I solved a few examples...
then, I listened to this again: Now its the best explanation that I can find anywhere!

[harshmishra]

Best explanation i have ever seen on this method.

[jessrevill]

Well explained.  I could actually follow it, and it's been many years since I've studied this.

[zackmorelli]

Fantastic video! Much more detail than my math methods book provides.

[jaredjones]

Underrated video. I wish I could like this another thousand times.

[mahdiaudujanda]

I appreciate your confidence in solving the mathematics problems thank for your action

[coal]

Correct me if i am wrong, but you solved this question with euler's method.

*Basically, if you can't write y in power series form, our point is singular.
*If you can also write down indicial polynomial and solve it, point is regular singular.
*You could put y=x^r and you could get the same solution.To use frobenius, you should've got recurrance relation.

[ethan]

Great video. After pausing the video and letting my brain catch up with you a couple times, this makes sense now!

[JimehC]

excellent video! if you can make this intuitive to my sleep-deprived brain then you can teach anything. You cut right to the point and explain just enough background information to understand the process very well. awesome video

[snp]

Good sir, you are an absolute legend.

[akshattiwari]

Great videos, I really find your videos more useful than my college profs

[niel]

Don't know if it is the lack of sleep but that family show joke got me good

[Bubbletwist]

not mispronouncing or misspelling Fuch's Theorem because "it's a family show" lmao
anyone spending quality time with their family watching this video is a maniac and the situation should be investigated.
Anyways, great vid, I love the explanation and the bits of humor, youre helping make this degree marginally less painful!

[sharkdavid]

Learning how to solve series solutions about a regular point was is an extra credit assignment because it wasn't covered in my class. Thank you this was helpful. However, one difference btwn SS-OP and SS-RP that I couldn't explain was when we took the derivatives of the respective series substitutions (i.e. y= sum(n=o)cnx...). Why did n increase in SS-OP but stay 0 in SS-RP?

Example:
SS-OP
y= Sum(n=0)...
y'= Sum(n=1)...
y''= Sum(n=2)...

SS-RP
y= Sum(n=0)...
y'= Sum(n=0)...
y''= Sum(n=0)...

[jacobsnoises]

Hi Khan! Great vid. thanks so much. One question, when you said "the radius of convergence for the power series is at least 1" at 2:38, don't you mean "at most 1"?