Taylor and Maclaurin Series
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- Опубликовано: 21 июл 2024
- Let's wrap up our survey of calculus! We have one more type of series to learn, Taylor series, and special case of those called Maclaurin series. This utilizes differentiation, and you'll see some familiar polynomials in this one!
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most math channels on youtube spend like 25 minutes rambling before they get to the actual point, this dude always keeps it concise and straightforward and it boggles my mind how much easier it for me to learn with his vids than anyone else's. cheers mate
I started from lesson 1 and finished now. I couldn't even solve the simplest algebraic equation and even had trouble doing some arithmetic. Now I can even do calculus. I am planning to study physics so I decided to go through the math playlist first, and then the physics playlist. Thank you so much Dave, you are a really awesome person. :)
yes and it feels like completing other side quest and then go fight the boss
cant thank you enough for this video. I went to khan academy, and 3blue1brown and didn't understand a thing, finally, before I gave up on it, I came to your video and understood everything. You made it way easier and simple to understand. You are a very talented man !! thank you. !!!
Hamid Alrawi I did the same and agree completely
The 3blue1brown video is aimed at people who already have some prior knowledge about Taylor series.
3blue1brown was teaching philosophy not mathematics
3blue1brown is for people that have already some prior knowledge on the topic or have slightly above average intuition skills, clearly you aren't one of them.
@@ayushdugar1698 whom are you intending?
I have my final exam in about three hours, the air and water show is in town and there are F-16 fighter jets with full throttle roaring overhead, my neighbor is blasting loud music so I can barely hear anything, and yet your video somehow managed to help me understand this concept while all that was going on. I love you, Dave.
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Your layout is soooo clean. So simple and straight to the point. Thanks so much
let me tell you, your videos are crystal clear and very helpful. never stop man. you are great. PEACE
deeppatel9623
Fortunately, it seems like he's going strong as ever now!
These knowledge gains can be. 👌🏾
Well, I think I found my new favorite tutoring channel. This helped me catch the concepts I couldn't quite grasp, and I really appreciate it.
Coincidentally, I just thought about this series this evening.
And now open youtube with your video.
Thank you so much.
It's not coincidence, it's called surveillance
I don't find any words in telling u how clear and simple u make the videos .. lots of respect and love to u !!
I’ve watched a lot of videos from other sites struggling to get an intuitive understanding of the Taylor series. After watching this, I’m finally getting it, and finding Dave’s other videos just as great.Really helpful, thanks so much!
I think man you are god gifted teacher. The world needs your lectures, keep it up bro!
I watched this video 2 years ago and untill watching this video now, I was unable to understand this simple concept (maybe my overthinking was making it difficult for me to understand this) but now, that I am watching this one day before exam, I don't know why but this just feels like a piece of cake. Your teaching style is excellent and I don't know, the pressure of exams really makes me go on flow state then i guess...
Professor Dave, this was amazingly helpful! Thanks so much!
ohh professor dave you are naturally ahead.... this video makes me clear understand about taylor's and maclaurin series
This video has given me some hope to not give up just yet.
This is excellent! Simple and concise explanation to a tricky concept
Professor Dave you really save my life!
Oh Dang, this was the last topic of the series? That's bittersweet. I'm happy that I have finished this Calculus playlist but I'm sad that I would need to find other channels now for even more advanced Math. But hey, it was still a fun ride. I'm glad and happy that I was able to finish this playlist.
Been watching you as my guide for my class discussion. Great job Prof. Dave. GBU
Thanks man. Only video that explains this topic clearly.
what the hell is going on, fml
this is so intuitive! thanks a lot
Great work professor,you helped me understand
Thank you
Really helped out. Thank you so much
Great Video! It really helped me understand the rationale behind the Taylor and Maclaurin series. I really appreciate the content.
I'm sending this to my whole class, I just found a new knowledge Bank, thanks professor 🙏🏿
Searching for this topic in the German RUclips Math space didn't do me much, I found the explanations of the Taylorreihe too confusing. So I decided to search for the Taylor Series in English, and thankfully, Professor Dave covered it, and I can finally understand the concept now.
Truly a legend, thank you lots ❤
A full 2h Course down to Just 9 Mins , a tip of the hat to you , thank you
Helped me understand it precisely. Thanks 😘😊☺️
I've done well in studying Calculus so far, but I find this topic quite challenging. Thankfully, it is finally starting to make sense to me, due to Professor Dave's more streamlined approach. Too many instructors think you must know the entire history of China before they can show you how to make a cup of tea.
wow, a month later i finally get this
Thank you for this
Thank you so much, this video was a lifesaver!
I love this video. Very clear. Nice job. 👍👍
Very beautiful. Thank you.
You explain very clearly!
Thanks a lot professor you’re literally the only reason I understood this topic
thank you sir, I love the way u explain mathematics...
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At first thanks to you. I did understood this topic before i saw your video.. Now this topic is very clear as like as water. Thnaks again sir..
Lot's of love man. You are the bomb! When I was watching your video, I couldn't help nodding. I was just like "mmmm Math makes sense after all".
So clearly explained. Please also cover Laurent series. I have the bell icon on
should the Taylor series in the first checking comprehension drill be just ln x?? because of the zeroth derivative
This taught me the logic!! Thank you so much
Great video, thanks, wanted to point out at 6:01, it should be a=0 and not x=0 for Maclaurin series.
really helpful, thanks
Super helpful video!
i have a test in the next 70 minutes, thanks for this so much!!!!
Why can we plugin 0 as a to generalize to the cases when a equals other numbers?
Where do I donate? You've made a significant difference on my understanding of calculus and physics. Keep pushing out videos please!
Glad to be of service! You can go to www.patreon.com/professordaveexplains or feel free to send any amount you wish to the PayPal account associated with professordaveexplains@gmail.com thanks for your support!
@@ProfessorDaveExplains done! I'll be sure to spread the word about your channel. I appreciate you!
Brilliant explanation, but also how do we call "a" in this topic, when we say function is centered at a=1?
Basically it's f(a) and as it says centered at 1 so f(1) so like it says nth derivative of f(a) so first you find the derivatives then plug in the value
amazing! finally understood this
OMG this is so much helpful
Well explained sir.Thankyou
Waaao sir great demonstration, u hv made it clear and easy for students. thank you very much
Do you have a video tutorial on Lorentz series?
finally understood thank you so much
thank you so much!
Thank-you pro it's very helpful
Derivative to e^x is e^x yes this fact we know from Maclaurin series, but we want derive e^x by using Maclaurin series we get infinite loop logic.
Thanx Prof. Dave! 😊
Omg thanks Math Jesus
Thank you
Isn’t the coefficient of c4 supposed to be 24 for the second derivative instead of 12? The coefficients are virtually factorials, aren’t they?
Hey, im a young student and i am passionate about this type of math. I just noted one thing that I didn't find coherent. At 1:18 in the video, you say that the remaining sum is C0. This is so because you calculate f(a). But when we develop the serie, the first term is C0(x-a)^0. What isn't explained is that you consider that 0^0 is 1, when it is actually an undetermined form. Is their any explanation that I dont have which would make me understand this better?
Great video Prof. Dave
I've learned a lot , but there's something you forget with the Checking Comprehension (number 2 problem)
There's no , P_0(x)= f(1)=2 🌺💗
Thanks so much!
excellent way of explaining. I got amazed with your explanation and did lot of calculus sums. Sir I will be sending very special 4 questions through email to you. Please be kind enough to reply. Interestingly waiting for your explanation . Thanks
i think i love you professor dave
In the second comprehensive problem why we did not evaluated f of a in the first term
Thank you man
Thank you sir
finding this before my calculus exam being like, wait this isnt discovery institute but its still Dave
OMG this video explain the whole thing incredible clear🎉
concise video❤
Thank you so much
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thx prof dave
have not understand that befor🔥
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better than the calc prof i pay 1.5k a semeseter for smh
this is the same way we get all trigonometry series mostly used sin and cos
8:10 I need the reason why the radius of convergence is infinite not negative infinite as it is less than 1
This hit different
We were taught this in College on this Thursday 😃
Mine today
i like how everyone is saying you make this simple and easier to understand yet im still extremely lost
you are an absolute LIFESAVER, God bless 🤍
Very good
Thank u so much
Go ahead sir :)
Thankyou sir
Thanks a lot🥲
I got sigma (-1)^n-1 * (x-1)^n / n for f(x) = lnx Taylor series at a=1?
I got sigma (-1)^n-1 * (x-1)^n / n x^n
why does the constant get an n subscript? Like whats the point, if its a constant, why not just leave it as c?
Because you have multiple instances of constants, and you name them all C with a unique subscript. Cn refers to the nth term's constant.
3:54 Do you really want any C4 in your series?
What a intro man...!!
If a Taylor series converges, is it possible that it converges to a limit not equal to the value of the function? Will anyone please tell me?
The Taylor series of a function f(x) around x=a does not necessarily converge anywhere except at x=a itself, and if it converges, the value at x is not necessarily f(a).
Look up the definition of an analytic function, and correspondingly, a non-analytic function.
The Taylor series will only converge to the function, when it is an analytic function that is infinitely differentiable.
Book reference?
keep it up
8:50 hi everyone. Where do coefficients 5 6 4 1 come from?
We evaluated that its derivatives are:
f'(x) = 4*x^3 + 1
f"(x) = 12*x^2
f'"(x) = 24*x
f""(x) = 24
Evaluate all of these at x=1:
f'(1) = 4*1^3 + 1 = 5
f"(1) = 12*1^2 = 12
f'"(1) = 24*1 = 24
f""(1) = 24
Now divide each of these by their corresponding factorials:
f'(1)/1! = 5
f"(1)/2! = 12/2 = 6
f'"(1)/3! = 24/6 = 4
f""(1)/4!= 24/24 = 1
It's zeroth derivative at x=1, is zero, because the original function is x^4 + x - 2, which evaluates to zero
Thus, we get:
T(x) = 5*(x - 1) + 6*(x - 1)^2 + 4*(x - 1)^3 + 1*(x - 1)^4
Since this already is a polynomial, it's really redundant to do a Taylor series. Any application of a Taylor series, could easily be done directly with the original function. All we need to do is shift the original function, so its input is centered on x=1.
Given:
f(x) = x^4 + x - 2
Let X = x - 1, and rewrite it in terms of capital X.
Thus: x = X +1
(X + 1)^4 + (X + 1) - 2
Expand & simplify:
X^4 + 4*X^3 + 6*X^2 + 4*X + 1 + (X + 1) - 2
X^4 + 4*X^3 + 6*X^2 +5*X
Replace X with (x - 1), and reverse the order:
(x - 1)^4 + 4*(x - 1)^3 + 6*(x - 1)^2 + 5*(x - 1)
Result:
f(x) = 5*(x - 1) + 6*(x - 1)^2 + 4*(x - 1)^3 + (x - 1)^4