Christine, this is madness!

If your evaluating at 0 shouldnt it just be called a maclaurin series? Initially I was confused because there was no number to evaluate the derivatives.

Spoiler alert: The Taylor series of a polynomial is the polynomial itself.

I am begining to undesrtand taylor now that i am 61

Professor Breiner thank you for explaining the Taylor Series of a Polynomial and it's relation to the Quadratic polynomial in Calculus II.

very clear and good refresher. what helped me when I learned this a couple years ago was writing out all the factorials (even 0!) as it shows people learning where everything goes and how to think logically. A lot of steps are skipped in the learning process on the second chalk board like f(o), f'(0) and the factorials. I didn't do math at A-level, so those steps helped me a lot when learning.

Excellent production. I can understand the speaker and read the board. Hell, that is more than I got from sitting in some classes. Great job, thanks.

It saved so much of my time at being confused. Thank you Christine. :)

Excellent illustration in the same way I expected and understood fully well !

First explanation that starts with the definition of the Taylor series. Good job. Nice video. Good pronunciation too.

Thanks for this video, MIT. It's my first time introduction with taylor series and i found my solution with the help of this video. Thanks again.

Thank you so much. This is the best explanation i've seen so far.

That was very helpful ! After all the purpose of using a Taylor's Series is to approximate a non-polynomial function into a polynomial one for easier computation, integration and differentiation at any center of expansion (x).

Wow thank you for the subtitles, I forgot my headphones and my campus computers don't have speakers.

I just gotta say that you are the best math teacher I've ever seen! Thank you so much :)

You are just amazing , very clear and easy to understand!

Amusingly instructive, and ultimately inductive (leading to a useful generalization).

thank you a lot for your good efforts and hope you all the best

Simple enough. What I've notice is that Calculus isn't too hard, the part that can be challenging is understanding it. Every-time I apply myself, and learn something, I end up amazed at how simple it really is.

Thank you Christine

you are so great at explaining Calculus. Thank you so much!

The lights starting to flicker, thank you.

thank you, thank you, thank you, Christine Breiner this is what I needed to see. thank you so much. I had been trying to figure out how to understand why this approximation is possible and I had the feeling that this might bee proven somehow.

Wow....It is amazing.Tommarrow is mine exam and Taylors theorem is one of the important for me very much.Thanks a lots from a son of Mother India

So much its so clear now and thanks for the good work....

I'm starting to understand Taylor series. Thank you very much Madam

Christine! Thank you a lot

This was great thanks christine

Great explanation ma’am thank you so much

Perfect answer... thank you.

Epic and Magnificent tutorial.

Awesome video. Gauss bless you! By the way @ 5:30 Madness? THIS IS SPARTA!!!!!

I Really Like The Video From Your Taylor's Series of a Polynomial Instructor: Christine Breiner

for a polynomial the derivative of X^n= n*x^n-1 so if x=3x ----> the derivative is 3*(X^n)= n*3*(x^n-1) the sum derivatives adds together so the derivative of 3*x^3 +6x = 6x+6 evaluating 6x+6 at f(0) = 6*(0)+6=6

You outdid yourself today. Thanks v much.....Great vedio.

Excellent explanation!

You're wonderful!

@patrickJMT in fact, it should already be allowed

Mathematics in its simplicity can be so beautiful. Brook Taylor and people before him are artists of human logic.

You are a good teacher

Thank you so much!

Thank you.

Omg this video was amazing

Great job.

U saved my life 🙏thank u so much 💯❤

Thank you !!!

I don't know this person but I am sure she is +12 now. I am using this medium to thank you for leting me solve Taylor's whatever without actually writing the formula. THANK YOU SO MUCH!!!!!!!!!!!!! God, the formula is confusing the whole thing.

Wow this is great i learned Taylor's theorm in 8 minutes...

lol, I didn't see that coming. Thanks, the video really helped me understand how to use Taylor's Series

Excellent explanation! While it is true that this is a Maclaurin Series (strictly speaking), it is technically Taylor Series since the Maclaurin Series is a special case of the Taylor Series centered at 0.

One of the many uses of calculus is to find the maximum value of something or the minimum value. In a diet you want to eat the minimum possible using a combination of X something. With this you create a function of X variables and calculus can describe to you the best combination to get the minimum value.

Amazing Teacher 😻

"This is madness!"

"Christine, this is madness" I LOLed xD Thanks for this video, very helpful :)

Never a dull moment.

"how do you prepare a nutritious food with calculus?" and how exactly is your equation related to calculus?

Thanks..your video was really helpful :) keep it up

this ladys explanation is a lot better than my teachers

Pretty cool material! (2020)

great video and professor :)

Well, that's how I've been doing it for the past couple of months now. That's how the course is designed. I think if you don't at least attempt the problem for yourself, then you won't be able to retain what you've learned.

the Taylor expansion for a polynomial is itself

i thought i was the only one who caught that! : ) maclaurin series is centered at 0; taylor is centered at (x-a)

Great class. i was wondering why I should do a taylor series of a polynomial, if my f(x) it was actually a polynomial... I was already expecting that, but was too lazy to try it out

oh you mean the Macluarin series !! first question that I asked myself was where is it to be evaluated

sure takes the long way home

Thank youuuu really you rescued me 😂

very fun...I enjoy it a lot.....

I love the chalk, I just love it

SHE IS A MAGICIAN :O

Thank you madam

@34comecome The taylor series is part of university level maths courses. It isn't used in everyday life.

@otterkicks no, your wrong.Maclaurain series is f(x)=f(0)+f'(0)+... so on. She use Taylor series but with "a"=0.

mindblown

Taylor's or Maclaurin's? Maybe im wrong...

Centered at 0 (notice how all the functions are evaluated at zero), that's why the answer is trivial.

MADHAVA SERIE ...BRILLIANT SOLUTION

I thought McLauren series was centered around zero? Where's the center?

i bet nobody tried it on their own when she left

:D :D welcome back, i like that.

The smile at the end😂❤

"at some point maybe you said...Christine this is Madness" "Well why is it Madness???" ~Because This is Sparta!

can i know how to decide the degree of the function??

mam hw many functions can we take besides u took 5 for calculating the expression

I want to know the integral of : e^x^2 please , & thanks .Thank you Christine

I love your teaching, can I find your own channel Dear teacher?

I LOVE YOU

wow, that actually helped me :D

which books would be better for algera and calculus

Genius!

Kristine you're the best wallahi

@otterkicks You are right! I did notice this too. The Maclaurin is just special case of Taylor for a zero argument.

at center = 0, this is maclaurin series to be exact

excelente explicacion teacher podrias traducirla en español

Polynomial functions are better to work with - for example you can work out the value of exp(x) or a trig function using a taylor polynomial approximation but without this polynomial approximation how else could you calculate this for any x? I believe calculators use the taylor approximation or a modification of this for example.

Nice! I like you! Even though you made me look like a fool for writing the function again.

god bless her

@otterkicks she did it because she is intelligent, because the tayler series will be exactly the same as the maclaurin series for a polynomial

Great explanation but I wonder if MIT students are not being taught the distinction between Taylor's series and Maclaurin series.

No deja de ser una serie de Taylor, la serie de Mc Laurin es para f(0), lo que no quita de ser una serie de Taylor. No longer a Taylor series, Mc Laurin series is for f(0), which does not removed from a Taylor series, generally.