Power Series - Differentiation and Integration - Calculus 2
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- เผยแพร่เมื่อ 31 มี.ค. 2018
- This calculus 2 video tutorial provides a basic introduction into the differentiation and integration of power series. It explains how to find the derivative and the integral of a function represented as a power series. In addition, it explains how to find the radius of convergence and the interval of convergence using the ratio test after differentiating a power series and integrating a power series.
Series Tests - Practice Problems:
• Calculus 2 - Geometric...
Taylor & Maclaurin Polynomials:
• Taylor Polynomials & M...
Taylor's Remainder Theorem:
• Taylor's Remainder The...
Power Series - Interval Convergence:
• Power Series - Finding...
Power Series - Derivatives & Integrals:
• Power Series - Differe...
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Power Series - Function Representation:
• Power Series - Represe...
Finding The Power Series:
• Finding Power Series B...
Power Series - Representation By Integration:
• Power Series Represent...
Power Series - Representation By Natural Logs:
• Power Series Represent...
Taylor & Maclaurin Series:
• Taylor Series and Macl...
Binomial Series:
• Binomial Series
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Parametric Equations:
• Parametric Equations I...
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I love how you don't skip steps, even if it's simple algebra. The supplemental videos for my class's book are garbage, they constantly skip tons of steps and often i have no idea how they get their answer. Thank you for not being lazy or arrogant to assume everyone in calculus has perfect mastery of Algebra
exactly. Some of the hardest parts on these is the simple algebra, for me at least
I know what you're trying to say but in your own comment you answered why some teacher assume everyone u know something... See one simple question takes almost 30min it'll take 100hr just to complete a small topic such as a single convergence test
fr like it will be like "given this series... step1: solve the whole thing"
@@AA-xu4vd i hate it
so im currently studying Bachelor of Learning Everything From TH-cam with Honours, thank you so muchhh u deserve all the love from this world
Best yt comment ever, try doing honours in comedy too, lol
My class is completely online and I've stopped watching my prof videos in place of yours. 😬 God bless you!
Pearson stinks
@Lacy Withenshaw whatever bro, since you're scamming bad people who wanna break into other people's insta, I can't say anything
@Lacy Withenshaw congrats, ur doing heroic work sir
My prof actually teaches really well but I low key slept through this lesson
dude ur better than Patrick and khan academy! I literally use u for all my stem classes and I've been doing so much better. Khan Academy is way too conceptual and Patrick focuses too much on examples ur like a perfect balance of both.
I love your videos. They have carried me through Calc 2 and now, Calc 3. Sometimes professors don't do a very good job of explaining things and your videos are a life-saver. I sent a link for this Playlist to my whole class (we are all struggling).
Unlike most comments, I have a wonderful math prof , but my prof always assumes you already know those basic stuff from book and she starts every lesson with a quiz and some hard af questions. and that is why I always use this channel to preview materials in order to survive the hard af lessons...
This is a great video. Thank you. You go through the entire process and show all your steps. That is so valuable. Again, THANK YOU!!!!!
Thank you , thank you , finally because of you I can understand series 🥳😊❤.God bless you ! I am so happy !🤗❤
Patrick and khan academy are also appreciatable , but on the other hand , u are also flawless♥️
your channel has helped me so much. Thank you!
You deserve all the good things in this universe! 🥺❤️
Thanks so much for your effort. I really understand it now!
11:22 notice when there's no n left to sub the limit
11:51 according to the ratio test
33:03 improper integral (integrated from 1 to infinity)
pretty useful, as always
at 24:40 shouldnt to be 1^n-1 as (-1)^n *(-1)^-1 (-1)^-1 was at the denominator
It's really helpful..Thanks alot.
Amazing video 😌
Constantly saving me from the demise of math professors with poor pedagogy. Thanks a lot!!!!!
very helpful thank you
This video will save me from my demonstration teaching on January 16🥰
Way better than my teacher lol
Thank you
Thank you!
Congrats on 1.6^2 million subscribers! 🥳
now he's at 5 million!
for 11:00, that problem can be done in one step with the root test by setting ((x-6)/4)^n :)
Skipped lecture today to watch your lecture videos lmao cus i knew imma sleep in the lecture Hall anyways so i came home, napped and now watching your videos, I don’t know if thats right thing to do 😭😂
Why do you always try and change it to (-1)^n+1, can you not use the alternating series test for (-1)^n?
y did u multiply d reciprocal derivative of the function in the ratio test, instead of multiplying reciprocal of the function? correct f i'm wrong. reply plz. thx
Wow!!!!Just WOWWW!!
sir i have no idea 👏👏👏
Thank u sir
My class textbook is very confusing so i just skim over it with a grain of salt then come here to actually learn the concepts. lmao
25 minutes on 1 problem. I hope to never have to see calculus again!
Holy crap these problems are long
does anyone know if he has a video about combining power series?
Does anyone know why each R value remains constant per each differentiation?? Please let me know.
It's a proved theorem that if you differentiate or integrate any power series, radius of convergence remains the same. I'm sure there are proofs online if you are interested
Goated.
Professor Organic Chemistry Tutor, thank you for another lengthy and Complex video/lecture on Power Series - Differentiation and Integration in Calculus Two. The examples are helpful for understanding the concepts; however, Constants of Integration are missing from some of the Indefinite Integral's solutions. Professor Organic Chemistry Tutor, at the 8:42 minute mark in the video, a Constant of Integration is missing after the Integration is computed. At the 28:33-minute mark in the video, a Constant of Integration is missing after the integration is computed. Please correct these small errors in the video.
Is there anything he doesn’t know??
If there is we’re all screwed.
You should simplify the factorials eg n/n! = 1/(n-1)!
by not passing the AST test, it does not mean the limit necessarily diverges
A class with out teacher
It's like a 🤖
Why can’t u use the divergence test to check if 10 works for the last interval?
Can anyone tell me why he changed the index to k=1 when he did f'(x) at 1:22 ? thank you !
Because the k=0 term is just 0. So he drops it by setting k=1.
Pay attention lol
3:42 I assume if we differentiate again the n just moves by 1 to n=2
8:35 if they r constants shouldn't they get an X as we usually do for integration?....
it's being multiplied
I dont understand the last part, interval of integration. Why did you take integral for 10, you didn't for 2
Bc for 2 he used alternating series test to test for convergence and for 10 he used integral test
They are different series and so they require different tests as Anepic said above.
14:59 if its geometric when are is greater than one it will diverge not r is greater than or equal to one
wrong
Okay
A sub zero? ❌ A sub scorpion ✅
Idk how my calculus professor got her phD they should take it away from her, every class she laughs about how her fellow prof are ahead of her in chapters and how we should quickly finish the chapters, not only that but every time she solves a question she solves it wrong!!! there’s no one lecture where we finished the lecture without her making a mistake and tells us about the mistake in the next lecture🤡.
Wow it felt good to say this she’s so bad that’s why am here🧎🏻♀️