Power Series Representation of Functions

[tRGodzApostle]

god damn i was enjoying calc 2 until god damn series and sequence. so many formulas to memorize wtf maynne????

[hazagawa73132]

how would you work backwards from the answer?

[KByunish]

@patrickJMT Hey so when you get interval of convergence, dont you need to check the end points? either they are inclusive or exclusive?

[patrickJMT]

@KByunish in general you have to check them, but here they will be excluded since the original series has | x | < 1

[KByunish]

@patrickJMT THANK YOU!!

[KByunish]

THANK YOU SO MUCHHHHHHHHHHHHHHHHH

[f0ckt]

That "am i pretty or ugly" video in the sidebar is one of the most strange videos i've ever come across on youtube, how it relates to proofs of power series functions i have no clue.

[patrickJMT]

@f0ckt they probably added a patrickjmt tag to get all the views. (just joking of course)

[WhaChuGoNaDo]

What are the integral of convergence for the last two examples?

[holypigsxO]

omg, soooo much easier when you explained it!! you're a lifesaver!

[TaraLynn218]

How do you find the interval of convergence for the last one? I have a hw problem I am working on now that ends up with x^(3n+2)/a^(3n+3). I have no idea how to find the interval of convergence if there are n terms

[duhboss1]

Patrick, I like you so much better than Sal Khan. I'm sorry, but those videos of his are super annoying to me. Thank you for your videos.

[MohammedShiekh]

i think you made a mistake in the last example

it should be "x" to the power (2n+2) not (2n+1)

[MrKenken2121]

I had so much learning in all of your videos, thanks for much. :)

[xxkisses4u]

calc final in two and a half hours. thank you so much patrick!!

[joemalorx]

patrick, my main dude

[gl9east]

do you have to check the endpoints to see if they converge as well?

[cwpix09]

Thank you Patrick for allowing me to be sane during finals week

[patrickJMT]

@cwpix09 glad i could help you keep your sanity :)

[immaturex3]

thank you so much for your video.

it is possible for you to explain how to get the power representation of 1/(3+x)^2

[Militant183220]

@immaturex3 You find the integral, which is -1/(x+3). [ if integral didn't help you find derrivative]

It become (-1/3)*(1/(1-(-x/3))

so the series rep. will be sum from 0 to inf ((-1)^n (x)^n)/(3)^(n+1) & the whole series multiplied by negative. still not done

We differentiate the series with respect to (x)

The series become [sum from 1 to inf ((-1)^n (n) (x)^(n-1))/(3)^(n+1)]*(-)

if you do index shift, it become [sum from 0 to inf ((-1)^(n+1) (n+1) (x)^(n))/(3)^(n+2)]*(-)

[LocalStrongMan]

do you get paid for the advertisement that infiltrated this video?

[ParsVid]

Patrick why don't you just apply for YouTube Partner and do the whole quick lecture and examples in the same video? thumbs up so he can see it!!!!

[patrickJMT]

@ParsVid the whole quick lecture? mainly i keep the videos short cause that is what people seem to like

[ParsVid]

@patrickJMT No I mean, like you know how you have like part 1,2,3 etc. Just do the quick lecture in like a minute or two, then do all of the problems for that lecture in one video. I'm just suggesting, but I love your videos and I'm thankful for them. I just took my Calc 2 final and some of the problems in your videos were on my test.

[runeruly]

you should teach professors how to teach

[Mrdisaster09]

Who needs a textbook anyways????

[Josh1billion]

Crystal clear. Thanks Patrick.

[idster7]

question: on the last question, I was a bit confused by your pulling the negative out. The "-x^2" is within parenthesis, raised to the n, and it can become "-x" in parenthesis, making the exponent 2n, which is always even. why not dispense with the negative in that case? i would appreciate a clarification from someone. your videos are always great. thank you.

[jadedrakerider]

What do you do with the x when you're evaluating these? Do you just assume that they're 1?

[tajuara100]

You are a genius

[meena2r]

thanks a bunch...!!

[skatty14]

Yes, without you I think I would fail calculus...lol

[Gunman160000]

Thank you so much for uploading these! my teacher doesn't do a very good job of making sure the class understand the matierials, so she assigns us assloads of problems to do from our textbook to compensate for her lack of teaching.

[mrhozer]

Any idea on how to do this given an integral from 0 to x of inverse tangent of t?

Do I just take the integral and plug in x for t, and then do the power series on the answer?

[mrhozer]

My teacher explains this in a very long and complicated method for 2 hours where he writes out all the series, does a bunch of complicated factoring, then provides the answer.

The Book goes into some drawn out theories with some symbols I've never seen.

Patrick explains it a million times better in 10 minutes :)

[hockeyman50]

Youre a savior man! Thank you!

[fakwater]

Patrick!

You are the MAN!!!

[mg100192]

THANKS! you are great!! you should get my professor's salary becuase he confused me for two hours while you just taught me everything in ten minutes.

[Cohn1369]

what is the interval of convergence on the last problem you showed? is it (-9,9)?

[F3udF1st]

Anyone here use Robert A Adams Calculus? Man that book is f*cking impossible to follow, unless you have a video like this to help you get started.

[foreverdressage410]

Patrick, would you mind doing a vid where the center is some other number other than zero? Thank you!

[patrickJMT]

@foreverdressage410 i have

[foreverdressage410]

@patrickJMT Thanks! I guess I didn't see it before :)

[ElGozz]

@patrickJMT Can you point me in the direction of the video you made where the center isn't 1? You just have so many and I don't know what it could be called.

Thanks

[ieatpoocrapshit]

if my professor watched your videos, i think he would learn something such as how to teach.

[MrCuffYourChick93]

you videos are so helpful youre a god..one question...how do you calculate the power series of f(x) using the method of dividing one power series by another

[DumMeister]

@MrCuffYourChick93 1B2Y......?

[MrCuffYourChick93]

@DumMeister yuppppp lol you at uea? ive solved the question now :D but need help with another

[50Mrmasta]

If you were a chick... I would marry you!

[patrickJMT]

@50Mrmasta if you were a chick... i would probably stay away from you

[MrWesShaw]

@jordane76r already did! lol

[daemonpacman]

My study technique:  Watch a PatrickJMT video. Pause it. Open textbook. Choose a practice problem. Solve it while talking to myself in Patrick's voice. (It's nice to have my own room so I can do it without being heard.) Happy Halloween.

[patrickJMT]

@daemonpacman ha, that sounds like a good way. happy halloween to you too! : )

[patrickJMT]

@daemonpacman your channel is 100% awesome. i love it

[daemonpacman]

@patrickJMT The highest level of art available on the internet today. Still not as amazing as your channel though. That may be impossible.

[viralrox8]

is there a way of representing a function as a power series through division? please add random exaples like this video, thanx anyway!

[suny123boy1]

This guy is one of the best, he could replace most university professors easily.

[confusedpanda42]

Thank you! you just saved me from failing my math quiz!

[patrickJMT]

@jordane76r ha, go for it : )

[hippynesswoot]

Can you do the reverse? Like how to get a function from representations of power series? and also term by term integration and differentiation...please and thank you!!

[dantham1990]

thanks for these extremely useful vids

[jazzlover06]

I've got to say: that's the most street sigma notation I've ever seen. :)

[litaroad]

Patrick, you may be more accessible than my professor! Also, I wish youtube would let you make longer videos like half hour to hour-ish, like an actual lecture. Would be nice. So sad that I'm saying this seeing as how I pay something like 600 bucks just to go to actual lecture but hey, sometimes it's not enough...

[VictoriasSecret27]

........sergio sanchez.

[GulfCoasta09]

I have a cal 2 final tomorrow at 8am. this video saved my life. thanks patrick

<3 <3 <3 from Alabama

[qaylin]

I just home from a 2 hour lecture on the power series. About half way through I looked around an everyone had stopped writing and just looked extremely confused. I came on here and watch 5:47 seconds of this video and everything makes sense.

[2007060120]

THANK YOU SO MUCH..you made my calculus easy

[saraelleese]

this was so hard to comprehend in class but you made it seem SO EASYYYYY. where have you been all my life?!?!?!

[wakeupnice23]

I've been watching your videos for almost a year of math classes now and I have just now thought to say thank you. You teach as if the material is very fresh on your mind, not in some mystic, impractical manner. Also, I LOVE the way you respond to idiots on Youtube. Your comebacks have to be the funniest and most appropriate on Youtube.

[jackstorm777]

You sir, are freaking awesome. Since my Stewart calculus book is a pile of shit and barely uses any examples, you are my savior.

[suny123boy1]

@jackstorm777

THIS, I too have Stewart's calculus and section 11.9 is total shit.

[Odaydhoorre1000]

Thank you for this video. It really helped alot

[oldbucktube]

i love you powered by billion

[JinwYi]

patrickJMT, did I ever tell you how much I love you? You make a 3 month class seem like a 1 day class ^^. You are saving me right now from loads of stress haha

[missmele19]

your sigma looks badass

thanks for the help!

[powage]

How could anyone dislike this? This is the best Maths tutorial I've ever seen online - no rubbish, straight in there, with plenty of examples to ensure that it's fully understood. If they still had the star system on YouTube, this would easily be 5* from me : )

[GohansRiceBall]

Very helpful videos. Thanks for all the examples!

[MultiNature]

What is the interval of convergence for the last example?

[waseem2010psut]

can you clear for me why you multiplied by -1 with the absolute value to get the interval of convergent ?

[SuperWrightstuff]

YOU ARE THE REASON I AM PASSING CALC III

[Militant183220]

@SuperWrightstuff Cal 3? that's Cal 2

[molitatron]

@Militant183220 thats cal 1

[Militant183220]

@molitatron in what university is series and sequances considerd as cal 1?

[molitatron]

@Militant183220 The faculty is called Instituto Superior Técnico ( Institute Superior Technical, translated by word, but obviously that is incorrect) of the Technical University of Lisbon, Portugal (where I study Computer Engineering/Science). It is arguably the best engineering faculty in Portugal, but nothing special internationally, i´m sure that a lot of other faculties also teach this in cal 1

[MadeInHK431]

incredibly helpful :) watching 2 of your videos covered the confusion of 2 weeks worth lecture

[Jartemeous]

So what would the interval of convergence be for that last example?

[samboni182]

Educator.com needs help marketing themselves. Kind of stupid to put their ads on videos that teach better than them. Its like an RC Cola advertisement on the side of a Pepsi can.

[ecazmusic]

@samboni182 RC cola kicks ass though.

[liangsupree]

THANKS A LOT !!! :D

[durevel]

very helpful! thanks

[TheManLegend13]

For some of your examples, wouldn't you need to check the endpoints of your intervals, some are conditionally convergent by alternating series.

[fighter91]

I'm sorry but the examples in this video are way too easy. You should've done some more complicated ones....

[BrianTheRoss]

Do you still find the interval of convergence the same way even if there is a constant in front of the summation sigma?

[kbattles28]

This video helped me have a better understanding on manipulating a power series. Very helpful.

[zanyareng]

niceeeeeeeeeeeeeeeee



[melissaonyou]

sorry, quick question, do you still need to check the endpoints after you've found the interval of convergence to see if either endpoint is included?

[mpsmonkey]

@melissaonyou I have the same question. Just commenting so I'll know when there's a response.

[guitarhamster102]

why you run out of time? I can look at your beautiful cal tutorials and your beautiful hands all day lonngg

[theyasin33]

Can anyone find the representation of 1+x/1-x ?????

[APlosh82]

haha same here alan.. just figured out some of my homework thanks to this guy

[alanr979]

Better than my Calc professor at the University of Delaware!

[poopeater14]

how about when you have something like 6/((1-10x)^2) ? i have been trying different techniques but i only got the first 2 in the series which are the function itself and the first derivative.

[youspinmerightrounds]

@poopeater14 I think that a function like that is singular and must be solved using an extended type of power series solutions called the frobenius method.

To test if it is singular, get your (second order equation) in form y'' +py' + qy = 0 multiply p by x and q by x squared. If you still have an 'x' below the line then it's singular and must solve the equation using a power series of y = An. x^(n+r)

[KGSultan]

16 other jealous teachers've seen this video ))))

[jpmiele50]

Why does MIT(video lectures) only teach series testing by integration?

[JaktheAtheist]

You are the best Patrick. Your videos are what let me ace calculus.

[JaktheAtheist]

You are the best Patrick. You're videos are what let me ace calculus

[JaktheAtheist]

You are the best Patrick. You're videos are what let me pass Calculus

[logueme]

you are such a badass...thank you so much, your videos help immensely in test preparation...

[stan021]

It is a very nice explanation....thanks a lot

[ebhjul29]

this just shows how much my calc 2 proffesor sucks

[thangbanhbao]

LMAO is it possible, to recordinate where they put the ads, it just ruins my train of thought and it SCARED the HELL OUT OF ME! lol

[ownedncut]

sit on my face

[ZidaTheBlazing]

You're awesome man. Every time I'm crunching before a test, I make sure to watch your videos to get another explanation and it's helped my test grades immensely. I like that you have a sense of humor too. Enjoy your champagne, soft bed of cash, and girls.

[vanished306]

WHERE HAVE YOU BEEN ALL MY LIFE

[rlyconfuzd1]

derive the power series for g(x) = (1+ X^3) ^(1/2) and put into sigma notation i need help on this problem

[l21thl]

Give Him Money, He Obviously has Earned it more than our proffesors. :P

[vishal075]

must make a fortune on the ads

[patrickJMT]

@vishal075 lol, yes, i am a millionaire already. i roll around my on my bed of $100 bills, while my girls serve me champagne.

[vishal075]

@patrickJMT Lol! now you know why i'm taking university math. 

[jadef7]

@patrickJMT lol really?

[superjokerrr]

@patrickJMT are you serious?

[Dino246810]

@patrickJMT After watching these videos and finding them so helpful, i honestly wish that upon you.

[Seanpitcher007]

@vishal075 Whatever he earns it ain't enough buddy. This guy is helping me become an engineer for free(I'll drop you $100.00 when I graduate Patrick... broke student here...)

[yozpho]

Alright... who clicked the dislike button?

[yozpho]

Alright... who clicked the dislike button?

[isleofairdawg]

you sound like a dog with peanut butter on the roof of your mouth

[1190641176]

I learn this lesson on Mon. and have test on it on Friday. It's very confuse . @.@ This video was very helpful for me, now i'm ready to take my test :) thanks

[hen555]

thanks man you taught me in 10 minutes what it takes 2 hours for my proff to teach...lol

[ISFKing]

greetings from planet jupter

[alkandoruk]

THAT'S IT. greetings from Turkey.

[Buniheart]

Thank you so much!!

[TheAnimal902]

Hey man can u explain me what is bessel function?

[krimzonstudios]

Thank you!

and a lefty too! =)

[remirap]

lol i got 3 ads watching this =(

[cadeskyler]

My profs will be ashame of themselves after watching your videos. Keep those great videos coming!

[cadeskyler]

You're good!

[jacobrichards91]

you make college calc so much better

[Sayuridesu]

This was SO helpful. You just made the textbook I am using in class and what the professor was trying to say crystal clear in ten minutes...You're AWESOME. <3

[EgoWafflez]

You teach this material better than my professor with a doctorate from Yale. THANK YOU SOOO MUCH!!!!

[kaymill9]

I made this youtube account just so I could comment you to say thank you so much for saving my math grade for the past two quarters of calc. I cringe to think about the $50,000 that my parents are wasting on barely decent math teachers, when I can watch these videos for free. YOU ARE AWESOME! and have literally gotten me (and some of my friends) through calculus. thanks!!!!!!

[XxmrsUchihaxX]

You are a life saver! If only I had discovered your videos earlier...

[iAttackPeople]

So can a divergent series as n-> inf converge on an interval like -1<x<1?

[xchocolatepagerx]

Hi, patrick i have an important question to ask you. I'm a student in UCLA and my professor told me that a is actually a constant and not the first term. i mean im confused. Please answer my question ASAP before my final :D thank you

[FroMaestro]

hey Patrick at around 3:19, why is that absolute value -1 that you factored out not just plain old 1? Isn't that what the absolute value does to the negative sign? Pls lemme know, thanks!

[CamocowProductions]

I like how the book only explains the first problem (1/(1-x)) and then throws in x's for the homework.

[dajakesta1234]

do u teach physics???

[guitarmast3r]

nice, i just saved myself an hour of staring at my calculus book

[707firedragon]

what is the difference between this and a geometric sequence or series?

[kellydelimon]

hi Patrick thanks for the videos they really help, i was wondering if you could help me with something, my teacher uses a very complicated method for solving this and when i came across your video i did the same example that he did in class using this method and got a totally different answer could you please tell me if i should have the same answer the example was 1/2-x c=5 his answer was (-1) ^n+1 (x-5)^n / 3^n+1 and mine was x^n / 2^n+1

[fafajardo09]

@kellydelimon yours is correct:D

[patrickJMT]

@waterspoutlake well technically you can start it at whatever so long as you as you adjust the formula accordingly. however, do not do that; start it at n = 0 as that is how the formula is set up to work : )

[InCase0fEmergency]

@patrickJMT If the series is undefined at n=0, should I start it at n=1?

[bnduong9132]

You should definitely be teaching my math class!!

[mynamesnotdan]

this really helps, at first i was clueless about the whole taylor series stuff but now it makes sense! Thanks a ton.

[ivar88]

THE BEST!

Greetings from Iceland



[patrickJMT]

@ivar88 iceland! i would love to visit!

[ivar88]

@patrickJMT It's a good place visit. Beautiful nature and great nightlife. If you are thinking about visiting Iceland let me know :)

[ivar88]

THE BEST!

Greetings from Iceland

[Krazyomni]

I wish you were my Calculus teacher. I have a fat sarcastic jackass for a teacher who gets mad when we don't know stuff. Great tutorials

[modelslist]

Can this be used if the center isn't zero? like c=3 or something like that?

[PolarisUSMC]

I wish I found your videos months ago. I'm expecting a C in my Calc II class. I would have pulled off an A in this course with no doubts in my mind had I discovered these sooner. I'm not joking when I say that I've learned more in to days of using your examples then in one month of my current Calc course. Though my instructor teaches from the book, and the book is only "good" if you already have an understanding of the material.

There need to be more instructors such as yourself.

[ghost433]

your a lifesaver

[Orab70]

"And now we have this good form". Love it. Thank you so much for your help. Got a B+ in calc II...I shudder to think what may have happened w/o your help.

[xDAZZE]

PatrickJMT should run for president. I'd vote for him because he obviously know how to help people who need help.

[Kaintdarogue]

Finals after tommorow, and these videos, are saving me A LOT of time in understanding the material entirely.

[jayr64]

i know you have heard this many, many times before... but THANK YOU PATRICK!!! you my friend, should be cited as a major reason for me ever getting my degree