Math is really hard when you trippin on walnuts.

"Sorry I just had some walnuts" lol

Nice math lesson, but the most important lesson we all learned is to always drink water with your walnuts.

"Sorry my brain is... I ate too many walnuts" -khan academy tutor

@SP-qi8ur

3 жыл бұрын

That's actually Sal Khan

"I hope this video gave you some intuition on the Taylor Series. If it didn't, please ignore this video" HAHAHAHAHAHAH BEST ENDING EVER

@nocturnalvisionmusic

Жыл бұрын

I was your 100th like! 🥳😁

What Sal does at 9:04 is one of the things that make it so easy to learn from him. He clarifies why he is using sin(1) even though it would be obvious to a lot of people. Teachers generally assume that the students know the reasoning behind every single step in their calculations, which isn't always the case. Thanks a lot, Sal.

@chantastlc

8 ай бұрын

9:04

Note to self: do not eat walnuts before exams.

Reading the comments before watching the video was really confusing hahaha

go bless you idk why I'm paying so much money for uni when I just end up coming here

@Glendragon

7 жыл бұрын

where do you have to pay for uni? FeelsGoodMan

@helmiazizm

6 жыл бұрын

So you could have a bachelor degree certificate to apply to some shitty job with it, duh

@ziyuchen3112

6 жыл бұрын

Cuz u need a motive for coming here to exhaust ur brain

@meeblings6

5 жыл бұрын

US and Canada for sure

@utsavshakya6891

4 жыл бұрын

@@Glendragon almost everywher except for norway maybe

i pay you nothing yet you teach me a lot. i spend all my parents saving to my university and i get nothing.

I want all my uni fees to go straight to you because you're teaching me more than any of my lecturer's ever could dream of

"My brain had too many walnuts" lololol xD

The next time I'm not studying for a calculus exam, I'm going to try and computer formulas eating walnuts. Sal, you're the best!

2nd video ive seen where hes choking on walnuts

I seriously can't thank you enough. My math professor's ineptitude is rivaled only by your competence in explaining the same material. I went into that lecture less confused than I was leaving, whereas this video provides a crystal-clear explanation. Who knows? If there were someone like you for every major subject, KZread could serve as a viable replacement for college. Cheers!

@bigpharts

Жыл бұрын

o/

Adding more terms makes the approximation of the function better at all points (not just at C). Even with just the first term, P(c)=f(c).

I like your funny words, magic man.

I did the former. Each added term contributes to the approximation and doesn't replace it. So the approximation with 100 terms would be much better than the approximation with 2 terms.

in 18 minutes you taught me a whole chapter of my maths book that my lecturer couldn't teach me in a 2 hour lecture. thanks sal!

this is truly amazing, with limited class time there is no way anyone can understand this shit. Thank you Khan Academy, for all the review.

Wow. This really helped me better understand the concept. I've watched another popular teacher on youtube, but visualizing it with the help of a software and the way you explained it, really helped me understand it better. Thanks

I can understand the effect of walnuts

Don't be sorry Sal, you deserve all the walnuts you could ever want for explaining this so well! I wish more people would take the time to explain the reasons behind maths functions, it makes it so much easier to see why and what's happening.

To answer a question that's popped up a couple times below: Doing a Taylor expansion for certain functions makes evaluating them around a certain point easier than evaluating the actual function. For example, doing this for sin(x) or tan(x) for SMALL values of x, the later terms of the expansion are so small that you can approximate sin(x) [or tan(x)] to equal x. Cool, right? Here's what I mean: en.wikipedia.org/wiki/Small-angle_approximation

I had the assigned notes on this for my calculus course, but I couldn't understand. I read it over, and over, and gave a week space in between so I can have a fresh look at the concept of Taylors Polynomial. I heard your site, checked out on how you were teaching the concept... and wow... best 18 minutes of my life spent ACADEMICALLY! Thank you.

How the fuck do people just come up with this stuff? its amazing

@alexhughes8211

7 жыл бұрын

With walnuts

@asp1346

7 жыл бұрын

Jesus

This is just fantastic! At my university I was only taught how to use the Taylor Series like it's some magical formula you just have to remember, but don't need to understand. In less than twenty minutes you managed to explain what exactly it is and how it is used. Thanks a lot!

this is amazing since, after seeing so many classes, and knowing that males are visual, only this guy decides to make taylor visual. Thx for putting "visual males" and "math" together.

oh my. Khan Academy's videos are something that i never regret watching! Best 18 minutes spent

This has been incredibly helpful-along with many of your other videos.

Thank you so much man! I didn't understand this concept well during class and this really cleared up Taylor Polynomial's for me!

khan saved my linear algebra and now my calculus too. thanks alot haha

this. is. amazing. I completely understand how taylor polynomials work now. Taylor was a genius.

I reviewed these videos again, and understand it now. Indeed, even the approximation at n=0, that is, where it's just a straight line or constant, is equal to the function at point c. Making the approximations better by adding more terms gives you better approximations at points "near" c and, with even better approximations with more terms, further away from point c. THANKS SAL!

Really Great lesson! So good! I recommend it to anyone trying to understand Taylor polynomials. Khan academy is amazing

amazing. i sat through an entire hour of this and learned literally nothing. then i watch this video and i understand perfectly. thank you kind sir

This was the most beautiful thing I've ever seen in math

@mokopa

3 жыл бұрын

Once you GET the Taylor Polynomials...it really does blow the mind into orbit for a while.

You have no IDEA how truthful that statement is.

Sir , i can't express my gratitude to you in words You help me a lot

nice work you have changed my attitude to the tailors theorem

Holy cow! This makes so much sense now. Thank you.

Had Numerical Analysis class for the first time at the start of semester today. He made me feel like a complete moron because he sped through Taylor Polynomials in class as if it was the simplest thing in the world to just pick up. This taught me more in 18 minutes than my teacher could in an hour and fifteen. Seriously, why can't more professors be this good?

Now you just taught me in 18 mins, what my Maths professor wasn´t able to teach me in like 3 lectures of 90 mins each! Thanks!

i love you. you are the reason a never ever have to go to math lectures/tutorials :D

Amazing love your voice, you tought something which none else taking about .

"sorry i had too many walnuts" LOLLL i died

@pravithandstuff1908

3 жыл бұрын

What’s good bro

you're amazing!!!!! loved the calculation part at the end

I Really Like The Video From Your Approximating a function with a Taylor Polynomial

You are blowing dust out of my 👂 , thank you

"my brain is a bit urgh, i ate to many walnuts" Educational AND amusing.. Win! ^.^

omg math is so beautiful ... and extremely well explained, thanks a lot !!

My exam is in 2 and a half hours and i only just learned taylors method from this video. thanks man.

thanks for the video. I like how you apply the equation directly into a graph, thanks

What I really think is mind-blowing is how you can write so clearly with a mouse. People can't even tell what I'm drawing on Draw My Thing, and I bet if you played that, you'd be drawing the Mona Lisa left and right.

How do you like them walnuts?

*Sal does a mistake* "Sorry I uh *stutters* My brain is really... I ate too many walnuts" What a classic line

Thanks, straightened the Taylor polynomial out for me in 20 mins... should have looked this one up sooner :)

Brilliant video - makes it so easy to understand :)

Tank you very much sir, very simple and intuitive explanation

how do power series differ from the taylor or maclaurin series?

4:44 - 6:28 Best two minutes of this vid for me :D

you save my life consistently

Love the video, thank you soooo much but there's one thing I don´t understand.. What's the purpose of the approximation when we already have the function?? dont get it... :/

@santiagoarce5672

5 жыл бұрын

In some cases you can use it because it simplifies the problem. Look up how it is used to calculate the period of a pendulum.

Aww thank you :) Exam tomorrow... This really helped XD

do you have any videos explaining the taylor remainder formula from Sal?

NOW thats the intuition behind the taylor! thx

May I ask you one question sir which software do you use to plot the graph ?

this 18 minutes teached me more than the 2 hours i wasted today in the school lyrbrary

omw thank you so much. u just gave me hope

Thank you very much. This was so much helpful.

Nicely stitched video. Taylor taylored a polynomial fabric that overwhelms the imagination. What is the meaning of an "nth derivative," for example? The graphs help you begin to see what's going on! Taylor Polynomials aren't just "sew sew." They are awe-inspiring! May the nth derivative be with you!

Amazing, had no clue what was going on until this video.

well done sir

Thank you SO MUCH This Got cleared !!

How can I get this graphing calculator ? It could be very helpful for my math extended essay if I can find it for free.

Thank you very much! I read the book but could not understand until I watched this video!

"I ate too many walnuts..." - Classic! Thanks for the help sal!

You make so much more sense than my Bus Cal 2 prof

This is invaluable, thank you.

wow thank you so much, my ap exam is in 3 days and i had NO idea how to do series before, just skipped all of the questions.

How can i expand sinx by validating power series expansion?

This is so cool!!! Thank you so much

8 words: thanks very much for this video. sweet explanation.

I never *saw* him type the taylor ploy into the calculator; I don't know if I "believe" you, mr.khan.

Remarkable Job!

thanks a lot, you did a great job of explaining! A+ Video

Could you possible explain the error term when approximating a function only to the nth derivative. I've got something about it in my notes but it doesn't really make sense to me.

which video has the e^(i*pi) = -1????? I WANT TO SEE THAT

thanks man i needed this

thank you so much...i just watched every series video and it makes perfect sense now. my ap calc test is this Wednesday and i was flipping out cause everytime i took a practice free response i just completely skipped the series question and was getting no points for it, not to mention the multiple choice. thses videos are great and e^(ipi) + 1 = o ...wtf?!

tanx for the lecture mr. khan, i like your teachin alot.... its helps me more than my boring ass lecturer

I don't understand how you come up with the values you use to divide the function (2, 6, 24). Could someone please elaborate?

amazing video, even in 2021

final calc exam tomorrow, never learned this stuff... combination of you + my book = win :>

thanks for this fun explanation!, a student from the future

Your presentation was fine. However, I would like to know why we go through the hastle of defining a function around a particular point for a stated function when we have THE actual function. I guess an application is in order so if you could get that on a video sometime in the not-too-distant future, that‘d be great. Thank you.

@domagojmarjanovic8824

6 жыл бұрын

It is used primarily in computing, to make calculations faster!

@passwifjreiguru5325

6 жыл бұрын

Oswald Chisala can you do cos(1) of the top of you head? No you cant. Thats why we use taylor polynomials. You can actually sit down and find cos1 with a reasonable degree of accuracy without a calculator when you use taylor polynomials. Also your calculator is actually using taylor polynomials to calculate trig functions and other weird functions like e^x when you put them in the calculator

definately confused me alright..what on earth do you mean approximate around c?

love your videos!!! thank you very much!!! Knowledge is for humans!!! :D... greetings from mexico

Thanks for this.

@someonetoogoodforyou The nth derivative is not equal to the function. It's equal to the function at c. As the nth derivative approaches infinity, not only does p(x) equal f(x) at c, but some of the terms near c of p(x) are close to the terms of f(x) near c. The more derivatives, the closer the values near c of p(x) are to the values near c of f(x) and the farther from c you can approximate. Theoretically, taking infinite derivatives will make the two functions equal for all x.