Taylor Polynomials

[Tanai7]

Hey sal, can you upload some videos where you do the ratio test for a taylor polynomial?

would be much appreciated :)

[Massacrist]

Why can't my maths lecturer explain things this well. He takes 10 times as long to teach us absolutely nothing.

[melisantika]

I am very happy to see the vidoe Approximating a function with a Taylor Polynomial from you, hopefully the others also are happy for You

[Onepissite]

I am very happy to see the vidoe after you give this Approximating a function with a Taylor Polynomial

[Ondelendo]

I Love The Video Approximating a function with a Taylor Polynomial It Can Increase My Knowledge

[bebeheuy]

Steady I Really Like This Video Approximating a function with a Taylor Polynomial

[willamricard]

Nice Video That You Share , So Very Nice Thanks You Approximating a function with a Taylor Polynomial

[imegatrone]

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

[anakmudajaman]

after i watched this video Approximating a function with a Taylor Polynomial, my insight is very open because the video is very good to give information

[kojelja0]

U teach me here in 18 mins something I couldnt learn last 5 years. Hahaha...

[heyjack7]

I believe you

[appninja9828]

dude.... Thank you so much!!!

[EntertainmentERA]

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.

[GettinCocoa]

Thank you SO MUCH. I've been trying to understand this concept for too long );

[dbshxjo]

I LOVE YOU.

[PeKei]

Now, this was easy :D Thanks :D

[jerrypower]

Holy shit O.O

I've not gone to a single lesson we have so far because the teacher is so bad, and i think i'm about to pass the whole course just by your videos.

[hukedonfoniks]

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

[doobiebotha]

Math suck I hate it.

[someonetoogoodforyou]

Hey Sal! Amazing video. Why did you make the assumption that if the 0th, 1st, 2nd, 3rd, 4th, 5th derivative is = to the function, then it perfectly = the function? I get the intuition behind it, and I can see it work very well on the graph. But surely there must be a proof, right?

[kckdude2]

@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.

[someonetoogoodforyou]

@kckdude2 Thanks for that kck. You're right, p(x) = f(x) at c if you take enough derivatives. But I don't understand how taking infinite derivatives will make 2 functions equal each other for all x. I can understand them being equal to either other at c or at c+epsilon or at c - epsilon. I think it's one thing to say they're the same at a point, but another to claim they're the same over the entire domain. I'm not saying you're wrong, I'm claiming I still don't quite get it :S

[BobcatBootyBeat]

Oh that's just great..now after weeks...countless hours...and lim (brainpain --> oo), I find this.

Great work!

[kcho0525]

thank you so so much.... my professor < you

[OZZl3]

What about the Lagrange Remainder! I understand all this but I can't make sense of lagrange remainder.. I know it's supposed to give you a better approximation but I don't understand the equation for it! How do you actually use it?

[SahaquieI3]

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

[jbsg01]

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

[markisfreshh]

Taylor Gang or Die

[THemoauveavenger]

Walnuts: the arch nemesis of learning calculus!

[freestyledavid47]

@THemoauveavenger deez nuts: the arch nemesis of learning calculus!

[supercalifragilismic]

closed caption ftw

[andrewtcb1]

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!

[Bashy14]

brilliant

[alisaffah]

what software he uses to plot the graph????

[Chat2Conaz]

@alisaffah Listen to what he says!!! He uses a website

[MeSooCrazyy]

@alisaffah the Snake Game

[alisaffah]

@MeSooCrazyy

i tought bomberman

[MeSooCrazyy]

@alisaffah @alisaffah haha,i thought you wouldn't get this joke^^,sorry :P

[alisaffah]

@MeSooCrazyy

no prob brother, i'm funny guy ;)

[MeSooCrazyy]

@alisaffah take care :)

[JcWongAndCompany]

Walnuts: The Kryptonite to all mathematicians.

[c4chus]

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

[MsOrangePen]

My school actually sent an email to everyone to watch your videos to prepare for our finals!

[KillenEMsoftly]

wow.....now i get it....thank you Master

[seekluv]

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

[Liaomiao]

walnuts lol, you should still try not to cough into the mic tho dude, great vid anyway

[avh129]

damn walnuts

[mirukufy]

Or their professor doesn't actually teach and just talks about hockey and Shakespeare the whole class...

[JThor001]

professor?? nah, i have a TEACHER. that's right, i'm in high school. get sum



[jkid1134]

@JThor001 I'm in 8th grade. I win.

[JThor001]

@jkid1134 That's too young... You don't need this stuff in Middle School---- child

[BlingBlingDubuLove]

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

[nigtasticbasedgod902]

THE SO ONTH DERIVATIVE!!!

[BoQuan22]

Just wanted to say, I bet the reason everybody is on this video is because their professors make it SO difficult to understand.

This makes it look SO easy so thanks again Sal =)

[harodon15]

Or their professor may be of Asian decent.... like mine

[RAF0769]

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

[Ichimaru666Gin]

tanx for the lecture mr. khan, i like your teachin alot....

its helps me more than my boring ass lecturer

[lightzebra]

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.

[hardpulse]

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

[marcsijames]

@hardpulse yes. the denominator in the terms of the taylor series is n! which is n-factorial. as an example say n=2, well 2! is the same as writing 2*1=2, as it goes, 3! is the same as writing: 3*2*1=6 but then again you proably realize this by now, as it has been a week

[JCP598]

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!

[MrAlexhusa]

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

[shiza223]

God bless you!!!

[myonlynick]

8 words: thanks very much for this video.

sweet explanation.

[billybaloop]

The graphing calculator is at url dot ie forwardslash 8kav

[tmtimi]

thank you!!!!!!!!! Im having my calculus final tomorrow and you saved my life!!!!!!

[yummyyop]

Thank you so much!

[Navt]

THIS SHOULD BE PRETTY NEAT! haha

[ny1fanta]

NOW thats the intuition behind the taylor! thx

[lexinaut]

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!

[freak1east]

I seeee. Its APPROXIMATING..A FUNCTION. Thanksss

[bennybonge]

u should have had some water with those walnuts!!!!!!!!!!!!!!!!!!

[sasamuraki]

lmao @ 'if it didnt ignore this vid...' srly who wouldnt understand after that comprehensive session... thanks heaps sal... thanks...

[tyler153796]

That was phenomenal! I am enlightened!! I wish I had known about khanacademy before struggling through all these calc lectures! Thank you sooo much! :)

[MrVoiceofreason123]

I would advise people to really learn Taylor polynomials as they show up a lot in later engineering and math courses. I'm watching this to be able to do my Diff. Eq. homework.

[angel209056]

"but hopefully that gave you some intuition"

"if it didn't, ignore this video."

HAHAH

really helpful, btw. reading from the textbook, it's hard to understand.

[duckboy81]

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

[kyjstout]

is there mouse lag for anyone else in these videos?

[expelliarmus007]

thanks, lots of help :)

[makmegs]

why cant you come teach at my uni?

[TotliTotli]

@makmegs Don't be selfish. Your not the only one that needs his help.

[makmegs]

@TotliTotli Are you being serious?

[TotliTotli]

@makmegs yes

[Kian0877950795]

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

[watchingstupidshit]

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.

[watchingstupidshit]

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?!

[battlenix]

THANK YOU. I'm struggling with my AP.

[E3tiger]

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.

[TimesNuRoman]

key to understanding calculus=walnuts!

[sammytsai]

thank you very much, big help on explaining, especially for a freshman first year =D

[13000000a]

o! so does the taylor theorem guarantee al function can be rewrite into a polynomial?

[13000000a]

thank you so much! bullshit at the end how can I possibly ignore this video you explain so well I totally need this!

thanks a lot!

[121212w]

Oh and Sal btw,

Brook Taylor (1685-1731) did not invent Taylor series and Maclaurin series were not developed by Colin Maclaurin (698-1746). James Gregory wa already working With Taylor series whenTaylor was only a few years old, and he published the Maclaurin series for tanx secx, arctanx, and arcsecx ten years before Maclaurin was born.

[OntologicalQuandary]

I thought cos x was a Maclaurin series

[deathbystarship]

"sorry, i just had some walnuts..."

glimpses into the mind of a genius. lol.

[valuhweeex3]

Thanks! :)

[g1code]

me to me : "congratulations , you are officially a person who understands what Taylor approximation mean at last !!!"

me to Sal : no need to thank you , I guess you know what it means to give the gift of understanding to another person

[MrNightLifeLover]

Basic but well done! I have to relearn multi variable taylor now..

[DarkSun260]

neat

[annie14411]

fantastic the best maths teacher

[thekaybee09]

thank you so so so much !! didn't make many of my 8:30 am lectures finals tomorrow !! you're a saviour

[13000000a]

@thekaybee09 lol mine is on wedneday

[saionjik]

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

[thepakman]

lol ahah me too. random question though cuz its insane we have a math final on the same day with the same stuff... do you happen to go to the university of saskatchewan? that would be kind of insane.

[saionjik]

Sorry, I don't I'm going to the university of south florida. Took my exam today, didn't feel so good as compared to my physics exam which i took earlier. We have the hardest tests of all the other teachers in my class for CALCULUS II and I think I've gotten a C or low B on the test. Okay b/c I got A's on my previous Exams! :D

[xxxcoolboyxxx]

Did you fail?

[SpawnZer0]

lol walnuts.

Another Masterpiece Sal, keep it up! :)

[Harrison716]

thanks : ) helped me big time.

[ncastle4]

I attend WPI and I still turn to these vids. Professors just don't explain enough the practical side of math or they submerge you in way too much math theory. Thanks Sal!!!

[roc788]

Things like this are the reason i love math

[saionjik]

Math rocks.

[guzzbar]

I love u

[Forestmyst]

nice, thank you

[whistlelana]

Thank you; I understand Taylor polynomials much better now. Could you possibly do a video on Taylor's formula with remainder and the Lagrange remainder formula? I need help understanding it. Thank you!

[videoofmike]

thanks! my text book didn't explain this very well and confused HELL out of me.

[Hampeps]

I love it!

[Ambarenya13]

"I ate too many walnuts..." - Classic!

Thanks for the help sal!

[02280228]

Thank you!! You are so awsome!! FINALLY I know why I have to learn this and how to use it!

[c00kiemonsters]

i love you.

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

[tfou3lakmara]

great job teacher -_-

[Dynamics18]

where is that proof of e^i*pi = -1?

[Poke4Poker]

part 7

[kurrizzle]

@Dynamics18 type it in you calculator dude

your mind will be blown

[lifeisgood070]

ok that helped a lot

But I still have trouble finding a degree. Like 3rd degree taylor polynomial of 2*Sin x @ x = (3pi)/2

[bll93]

THANK YOU!!!!!!!

[Ukapx]

bloody brilliant Sal.

This is how math should be taught.

[elburro1887]

thank you so much!! my math books are too theoretical for me, i cant understand anything in there ;), but your vids are helping me alot!

[ibizaboyz]

thanks so much! you're so much better then my professor :)

[postaboy506]

no more wallnuts for you! this video was great

[schnewitchen666]

Really great, Though I am not a native english speaker i finally understand it. Much better than in our university. please keep on doing those videos

[chrstnrnld]

nice explanation ,thanks a lot i knew how to calculate taylor's polynomial but i did'nt knew what it is used for ,please do a detailed lecture on curve tracing to trace curve of any type of function

[Dynamics18]

me too. They never tell you exactly why, or they brush over it puting far more emphasis on how to do it. Personally i think that way of teaching is rediculous. Whats the point of knowing if you dont know what to do with it?

[Ren520]

cool! =D

[Nanumir]

wallnuts!

[AakiBibo]

great, better than the teachers.

[gremlinextreme101]

couldn't agree more

[roshan2004]

How can i expand sinx by validating power series expansion?

[sikory]

isn't this a way to find the equation for the tangent line at a point if you just use the first two terms(term 0 and 1) and then do some simple arithmetic?

[diwr]

nice intuition btw!

[diwr]

mmm walnuts

[brco2003]

when u add each term, are you adding it to all the other terms or are u just graphing it by itself? that is, was the second approximation p(x) = cos1 - sin1(x-a) or was it p(x)=-sin1(x-a)??? i think ur doing the latter... in which case, wouldn't the, say, 100th derivative be a really small constant times (x-1)^100?

[khanacademy]

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.

[brco2003]

oh okay... so ur really just adding more terms to the approximation, not coming up with completely new and different ones. So let's say f(c)= 5 for example... so p'(c)=3, p''(c) = 4, p'''(c)=4.5, p''''(c) - 4.8.... and p'''''''''''''''''(c) = 4.99999999.... IS that kind of how this works? each new approximation corresponding to a higer derivative will be a better approximation of the value of the function, at point 'c', than the last??? am i getting it?

[khanacademy]

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).

[brco2003]

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!

[brco2003]

thanks