When can you use Series to solve ODEs? Ordinary vs Singular Points
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- เผยแพร่เมื่อ 8 ก.พ. 2025
- Series solutions can often be extremely powerful for solving differential equations, particular linear homogeneous ones whose coefficients are nice, what we will describe as being analytic in this video. But when, exactly, do these apply? In this video we will dive a bit into the theory of series solutions to solve ODEs. We are going to see that there are two types of points, ordinary points and singular points. For ordinary points we get a nice theorem that says not only do we have a convergent power series solutions, but also it tells us the radius of convergence is at least as large as the distance to he nearest singular point on the complex plane.
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I have realised that the more I watch your lectures better I am at understanding the key ideas you are outlining.
Well, I am glad to feel it that way, because it means that you are building a sense of intuition of understanding for your audience ( for me at least)
Please professor keep lecturing us even if I can relate how time-consuming it must be to produce quality videos like yours !
you explain so well and simple that i could listen to you all day
Sir. Want more more...... videos in series solution . We are always w8ing for ur lectures.
Finally going to complete just one more left Sir , After watching I can say its fantastic !!! I will also see the next series for sure !
THANKYOU SIR !
Great job Dr Trefor . . . really amazing how you explain these topics
You sir, have a gift!
Very helpful!
Very cool vids man. Thanks!
Great video, I actually understand it now, thank you!
DR. Trefor Bazett, thank you for an excellent video/lecture on When to use ODE? Ordinary/Singular Points. I am still processing this topic, therefore I will rewatch this video.
Thanks a lot dear sir 💛
You're most welcome!
I might have hope on my finals after all🙏
Why we always let the ordinary point to be zero ?
Why?
Amazing........ Extremely helpful for me... ☺
Glad to hear that!
that was amazing and i have just subscibe
sir your video is really helpful...but is the result of the redius of convergence is also true when we find series solution about regular singular point...? i.e. distance from its next nearest singular point ...!
Sir i have a question when we use series solution in 2nd order differential equations
I think we used when singular point exist.
I think we used when singular point exist.
Frobenius method is used..
Make some interesting graph problem videos on bridges and dfs
😮 I ignored that!
Sir , i think it is difficult ...i am not understand what does convergent radius means .... I am not visualised
It's trying to determine where the infinite series converges to a value (has a solution). Some eqs can only give values at certain intervals
Please make pde videos