calculus 2 power series, a detailed introduction (form, radius & interval of convergence)
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- เผยแพร่เมื่อ 29 มิ.ย. 2024
- This is how I introduce the idea of the power series to my calculus 2 students. The goal of a power series is to write a "complicated" function as a polynomial. We love polynomials because they are easy to differentiate and integrate! : )
For more power series examples and the power series representation of common functions, please see 👉 • Power series ultimate ... . (power series ultimate study guide)
0:00 introduction to power series
9:06 the things we need when working with power series
17:21 our first power series, aka, best friend! • BEST FRIEND
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Thank you,
When you learn more from a 30 minute video than you learn from online classes for the entire semester.
I've already passed calculus 2 but I always enjoy watching BPRP nonetheless. This guy makes math fun 👌👌
Thank you! : )
Always be excited seeing a 30 min bprp documentary-like video. I'mma grab some popcorn now.
What? 11 years ago?????
@@aashsyed1277 what's the problem? I'm his patron more than a decade ago. That's why
@@omniyambot9876 ok thanks your name includes 11 years ago
Same!!!
@@tzonic8655 I liked your comment
I clicked this video to see how a poke ball can help me learn power series and ended up watching whole video because of brilliant explaination 🤣 thankyou 😄
You are such a blessing, my calc 2 final is in two days and you explained this sooo much better than my prof!
I have my Calc 2 exam tomorrow and power series have been driving me crazy, this video is literally a blessing 😭
Thanks to you and your videos on infinite series and complex numbers I now understand how to implement DFT and FFT in computers. BPRP, you're up there with 3B1B as one of the greatest math teachers ever
If there is a math teacher like bprp in every college in the world, this world will definitely become a better place to live in and learn something meaningful and also learn it the easy way. BPRP makes math fun and easy to comprehend.
such a good channel. I love that you do things oldschool!
this is the MOST in depth explanation I’ve found!
I would be happy to see you using Laurent series as well
Dude where were you when I was in my FY of engineering 😭. I really wished that this video was available back then. But it's never too late to learn it in better way.
You are such a good teacher bprp, cheers!
Great motivating introduction = Great teaching skills. Thanks.
This is on another level thank you so much sir you explained it in a very amazing way ❤
You know what's weird? Periodic functions and the power series. Like, consider the power series for sin(x). The sine of 0 has the same value as the sine of 2 pi, but the terms in the power series are WAYYYY different. sin(0) just involves terms that all equal zero, but sin(2 pi) has got terms that go as high as 81.6 and as low as -76.7, yet somehow they all cancel out and you end up with zero anyway. It's freaky.
i can see that shin chan hanging there.....so cute and the best teacher for calculus :)
LOVE FROM INDIA
The golden giraffe there too.
@@beastgamer4932 yes 🤣
attitude is everything - thanks for your good attitude and epic personality, it makes the learnign actually happen and actually happen in an enjoyable maner :) you add a lot of value to my education
Ahh sir you are awesome, thanks for mentioning about the radius of convergence, which I haven't come across in my text book
More generally, it's actually about the property of basis. Power series is just a specific case of change of basis. Another case would be the Fourier series/transform which yields consequently, the same useful property of being able to just add the coefficients.
Bprp. That is the best introduction to power series that I have ever heard! Great job!
Thank you!
wow! such a great explanation
A 30 minute video! I'm pleased
I am too!
You watch bprp! I saw you from Sybermayh videos.
@@beastgamer4932 yeah im his moderator and i got my own channel if you didnt know
i love this man . Thank you !
This video is very interesting... coz i am a small family member of the topics you chose this time
Wow. Amazing. Thank you so much!
Thank you for this video!
"I know, please do not turn off the video" 😂😂😂relax, we trust you😂😂❤
Your method is engaging also entertaining
Thank you for the fraction to decimal analogy. I understand P.S better now
Could you please do a video about the derivation of the cubic formula?
Needed you when I took Cal2! Still give me nightmares 😖😖😖
Great video!
Thank you professor
i appreciate u so much...keep it up on
Interesting I am learning this as calculus 4.
"definitely we love polynomials because we can differentiate them, integrate them"
me who was skipping all calculus classes whole semester: 😰😰😰
This is Gandalf in his purest form. That beard is my savior.
i should say ..."mind-blowing teaching skills"
Wonderful...inspiring
bros the best teacher on youtube
Thanks!
Thank you, too! : )
thanks from ethiopia east africa
14:40 was a game changer
I like your vedios. Did you ever compute the sum of all integers represented as an imaginary number? Or the sum of all the imaginary numbers without the Real component?
For better explanation of Taylor series you can see video of 3 blue 1 brown.
You are doing great at maths, helps a lot. But, Why do you have Beard?
What operation did you perform at 5:00 to arrive to the new forms of e to the x and 1 over 1 - x?
Beautiful, absolutely beautiful Maclaurin.
My man talking about fractions that I understand, then immediately skips to matrices! XD. I'm just joking but thanks for the video! You inspired me to start my own channel and I love all of your content!
oh nah blackpenredpen linear algebra jumpscare!!!!! bro is switching genres!!!! lmao awesome video
YOU ARE A SAVIOUR!!!!!!!!!!!!!!!!!!
Hey *bprp fast/versatile/explorer* do you have some time for my request as I asked earlier. Even my birthday is near. Please think about it and reply.
Yo big fan.
Steve: Right?
Kevin: WRONG!
Ah yes the only part of calc 2 that I actually found quite difficult
Enjoyment diverges to infinity 🤝
excellent
I LOVE THE BEST FRIEND
Sqrt(2) + π = 41/9 :)
\approx
You cannot get a rational expression for pi
Addition of rational numbers is different than multiplication and a little bit more difficult
Hey I just got finished with a grade 9 unit on optimal surface area and volume, I made 2 formulas and plotted them on Desmos and found that for each value (a), they always intersect at (x= a^3 x pi) and (y= a^3 x pi). Here are the formulas I made, and if it helps they’re for minimum surface area for a given volume and maximum volume for a given surface area. Minimum surface area: a x pi(x/pi)^(2/3), Maximum volume: pi(x/a x pi)^(3/2). I would give photos but I can’t put any in the TH-cam comment section😂. It just popped out of no where when I was reviewing some of the past formulas I made. It would be great to see why this happens!
I'm studying math on my own. I'm stumped by this power series:
\sum_{n}\left(- \sqrt{n} + \sqrt{n + 1}
ight) \left(x - 3
ight)^{n}
I'm trying to apply the Ratio Test for convergence, but can't figure out how to reduce the limit involving radicals.
Help!
13:47 watch the "form" change into "Form" magically
Solve the JEE ADVANCE mathematics portion
Everyone watching this: learning
Me: So how exactly is he doing that with the markers??? Magic!!! So cool!!!
How can I integrate 1/(x^3+2x+2) dx?
integration by partial fractions
Please prove that parallel lines converge at infinity
xD
Calmest comment in blackpenredpen channel
@@jadeharley413💀
They don't converge
@@jagrit9718 yea now I know ...that time I was too young to understand.🙃
I almost fell over when you said why don't we teach matrices to 8 years olds😹😹😹
Why not? I never learned matrices since COVID cut my algebra class short 🤣
Maths topics shouldn't be tied to age. Anyone can learn anything at any age, as long as they've covered the pre-reqisites
you went from young boy to sensei in just 2 years...
Genius
Please solve x^x=2x
1+1 is 2 :0 5:40
My teacher,which country do you live in?
🖤✨️
2:08 Funniest part of the video
Missed opportunity to show that sqrt(2) = 1.1414 is just another power series representation with x = 1/10.
Can you solve this $ 3x(1+2x^2)^1/2 dx
when you have a best friend, you have to know how to use him ... It sounds so bad !! 🤣🤣
If |x| is not less than 1 then it gives many illogical answers. For example put x=2 in our best friend and you will get 1+2+2^2+2^3+....= -1 which doesn't make any sense. And at 23:26 according to Ramanujan 1-1+1-1+1-1+...= 1/2
1-2+3-4+5-6+...= 1/4 and
1+2+3+4+5+6+...= -1/12
I know that it doesn't make much sense but that's true according to Ramanujan.
About the Summation of all Natural numbers. The answer is indeed infinity. -1/12 is just a "better" and somewhat "logical" answer.
Consider a dirt full of random answers for the Summation of Natural numbers, and -1/12 is a Golden nugget in it. It's like that
73rd
Sensei
Please integrate :-
ln(ln(ln(lnx)))
I’m trying to do my Spanish homework… STAHP.
老師好
16:16 🤣🤣🤣🤣🤣
I want to translate these videos in Arabic, please❤️❤️
Just learn English
76th
9:57 what are you saying and drawing XD lmfaoXDXD
Is it possible sinθ > 1？or sinθ < -1 ？
吃叉雞囉！！
In complex world, yes it’s possible that |sin|>1
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RIP to those who think sqrt(2) + pi is 4.5555555555.......
How can I do math in 5 min.without knowing any rules ??????@blackpenredpen
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