Taylor and Maclaurin Series - Example 1

[ian559fresno]

You are a legend at my school. Everytime someone's struggling like math we hear "Watch PatrickJMT videos" haha

[patrickJMT]

@ian559fresno that is very nice of you all, i appreciate the love :)

[Darkarium]

Great video but something with your mic is making an annoying noise in my left ear. Like a faint breathing / rumbling.

[patrickJMT]

@Darkarium yes, old mic, old video.

[ranger0785]

Yea, gotta agree with everyone else, you rock man. Thanks for doing this, it really is making a difference for a lot of people.  I tell people about your videos in every math class I take. I know you make ad revenue off this stuff, but it's still awesome that you take the time to help the little guys behind you. Keep doing what you're doing because there are a lot of engineering, science and math diplomas out there that were granted partly because of your work.

[patrickJMT]

@ranger0785 i do make a little money from this, yes. but for the first year and a half i was doing it cause i wanted to help and that has not changed!

[kadir940]

thank you sooooooo much ... I love you man

[wowwowweewow4wow]

Wow! you are so much better than my teacher! LIFE SAVER MAN! Thank you!!

I was wondering if you had any tutorials about like vectors and things.. like stuff related to de moivre theorem and stuff? It fine if you dont, you dont have to make anything, was just wondering..

[patrickJMT]

@wowwowweewow4wow search, and ye shall find

[ignitionSoldierStrik]

Thank you so much for your videos! I went back to school after 10 years since my last math class which was Calculus. I went back to school and started off with Calculus 2 and the only reason I made it because of your videos. I appreciate what you do and I wish you many good tidings!

[matdamond]

marry me. im a guy and im not gay but still, marry me

[myterribletube]

can someone explain, where and why you would use this in real life,.. i need those who study physics to answer this, since math students have no idea, exept the numbers :)

[patrickJMT]

@myterribletube this stuff provides a super basic way to study and find solutions to differential equations. physics is full of differential equations; they are everywhere. the newtonian laws of motion are differential equations, for example (you do not need this stuff to solve those though). super duper useful stuff. just google it, i am sure you can find some stuff on your own without much trouble at all if you are really interested.

[MysterySultan]

@myterribletube A computer doesn't know what sin(x) means, but it does know what 1 + 2.1 + 3.2 + 4.3 + ......... forever equals

[alwysatthegym]

@myterribletube

I am currently using it right now in an aero design course. We have to find an accurate approximation for takeoff and climb performance of our planes. Many texts offer a simple equation to determine these performances but they are based off many assumptions. The taylor series is suppose to give us a more accurate representation. They also told use there was and almost always is a simpler way to solve an equation than using taylor series. Series are also helpful with orbits.

[toutankham0n]

good work, from egypt :D

[redpunk]

i always sucked at series. it's too bad they're so damned important

[axfndi62]

i survived calculus 1 thanks to patrick, but i'm glad im not taking calculus 2.....god, i dont wanna relive those days of sleepless nights and math terror.

[salomon0991]

i give you 9.9 of out of 10



[patrickJMT]

@salomon0991 i give you the remaining 0.1 out of ten

[salomon0991]

@patrickJMT haaa

[DaveBandfanMatthews]

@salomon0991

I give him a 10 out of 10

[DaveBandfanMatthews]

@DaveBandfanMatthews

Actually a 100 out of 10

[Sharpryno]

CALC2 EXAM CRAMMING WITH PARICK

[caligal2010]

Hi Patrick, just wanted to let you know, after weeks of watching your videos and studying my butt off, I passed Cal II with a B+!!! Couldn't have done it without you, that's for sure :))

Now, time to take on Cal III !

[McDreamy2009]

This is saving me and is a GREAT cram before my Calculus II final (along with all the rest of us :p). So thank you for doing this and explaining it in lay-men's terms :].

[faizzzzan]

i have my calc 2 final in 40 mins and im totally relying on patrick!! D:

[Billabong024]

Patrick, how do u know when to use the maclaurin series? do you think that on the exam a professor will specify a problem to be done using this particular method?

[caligal2010]

@Billabong024 My professor told us when to use the Maclaurin series. Both the Maclaurin and Taylor series are basically the same thing though.

[UltimatTacoman]

Thank you, so much for these videos. I already kind of understood this stuff, but this solidified it for me. Again, thank you.

[zeoxzy]

Tthank you so much for this, why can't my lecturer be you??

[Mig440]

This really doesn't help much, in finding Maclaurin series expansions for other than "nice" functions, ie. with "nice" derivatives.

[patrickJMT]

@Mig440 sorry m'lord

[da1booger13]

@patrickJMT

HAHAHA oh my goodness! LOL! This was hilarious.

[da1booger13]

@patrickJMT

Hahahha I've been looking for this comment! Hahahha it made me laugh the first time. Your sarcasm is just fantastic, man.

[patrickJMT]

@da1booger13 fantastic or obnoxious, take your pick :)

[mdtTheory]

@Mig440 He couldn't have done much more without doing the problem for you mate. This is sufficient for pretty much any function within reason.

[FermeJusqua]

Thank you so much, didn't understand 10 different sources till I found your video :)

[TheNumber2Pencil546]

amazing job like always patrick!

[p3rUvIaNSoLdI3r]

i wish i had found ur videos weeks earlier!! you're ten times better than my teacher!!! i won't fail my exam now, but at least i'll get a C  :(

[BinJim31X24]

I must say patrick, I love all of your witty comments to the ones that are trolling all your videos!!

[KingdomKeyEquipped]

I was freaking out last night, HOW AM I EVER GOING TO PASS THIS, ALL THE THINGS I READ ON THE INTERNET ARE TOO COMPLEX TO UNDERSTAND AND I WAS TOO CHEAP TO BUY THE BOOK?!?!?!?!?! Then I found your videos, and they literally saved my life. Thank you thank you thank you!

[9999sssu]

Finally....couldn't understand it that clearly from my teacher,but you've done great job,thank you so much.

keep it up, I may need you in more help in Numerical Methods course,thanks :)

[DaveBandfanMatthews]

You are the man Patrick JMT! Just saved me for my Calc 2 final!

[patrickJMT]

@DaveBandfanMatthews hope it goes well!

[limpbits]

@patrickJMT for sure dude thanks.bah i know the teacher knows her stuff, and i know shes a very nice person and a generous grader, or her TA is, but man, she cannot teach. laughed at the sigh at the beginning.

[jiiji1990]

10xxxx so much...i didn't understand this lesson until watching this vidéo :)))

[gaboonviper89]

Thank you for creating these videos. My teacher didn't want to help me out and I found these videos to be loads more helpful then her.

[patrickJMT]

@gaboonviper89 lots of sequence and series videos, so come back any time : )

[davisinful]

Great!

[rosaliehalevampire]

you're left handed!

[LlLChubby]

You didn't tell how that generic form popped out.

[patrickJMT]

@LlLChubby try watching the video where i do that. probably you'll watch one that and say: but you never used the formula to do anything.

[LlLChubby]

@patrickJMT

I know everything you did there but there was no explanation as to why f(x) equals such thing which appeared at start.It's kind of "memorize the formula".

[vincentli93]

@LlLChubby just stop. PatrickJMT is the man

[patrickJMT]

@LlLChubby once again, there is a separate video on deriving the formula. go watch that one. i also do not derive the base 10 number system in this video...

[LlLChubby]

@patrickJMT

Ah! now I catch that...I thought you're referring to this video of yours.Sweet dreams!

[xxsecretdreamerzxx]

what are you suppose to do if its e^(x/8)



[gingersteve]

@xxsecretdreamerzxx Cry?

[MonicaKn17]

Try crayon next. You haven't lived until you've done calculus in crayon. 

[patrickJMT]

@MonicaKn17 i never cared much for crayons

[AceAites]

Sorry if this is a stupid question, and it might be because I'm watching this way past 2 am, but why is the derivative of 5e^5x=5^2e^5x and so forth ? Thanks !

[patrickJMT]

@AceAites you should watch the video on taking derivatives of exponential functions

[gingersteve]

@AceAites The derivative of 5e^5x is 25e^5x, and for the sake of making things looks simple, he's expressed the 25 as 5^2 instead. If you think about expanding further through several more orders you'd had values of 125e^5x, 625e^5x and 3125e^5x within no time. It's just much nicer to express those as 5^2e^5x, 5^3e^5x and 5^4e^5x! Hope that helps.

[AceAites]

@gingersteve no, apparently the problem WAS because I was watching this while I was tired. I already knew this. Chain rule dicatates that you multiple the whole thing by 5 and since the derivative of e^anything is e^the same anything, you get 5^2 e^5x.

Sorry for the misunderstanding. I don't function well when I'm tired.

[gingersteve]

@AceAites No worries! I'm the opposite, I get all my best work done at 2am =].

[teshsherpa]

this helps!

[chulminh]

it's not right to blame your professors for the confusion. The materials your prof cover in class are some what new and this video is just a review of what you've already seen in class. If you were to watch this video first, without the lecture in class, you would feel the same anyway.

[yukun92]

Thank you so much. Your videos are really making calculus much easier for me and what seems like thousands of others. What will we ever do without you? :)

[patrickJMT]

@yukun92 ha, free quizzes with solutions on nixty

[RichardDorvilier]

Same here, thanks so much, you simplified my professors confusing 2 hour lecture into 2 videos. I really appreciate it! ^_^

[lllopoh]

very clear example, thank you!

[JstJAYMZ]

FUCKING ADVERTISEMENTS

[TheHarryThang]

Thank you so much. My hero :')

[deadpeng]

I have a question here. Am I right to say that not all functions can be expressed in taylor form?

[patrickJMT]

@deadpeng you are correct, not all functions have valid taylor series representations

[jessyjkn]

i didn't have a teacher or a class when i took the ap calc bc exam, but i got a 5 thanks to your videos!!! THANK YOU SOOO MUCH!!! Much appreciation!

[AhmedTouma]

Thanks

[shikharsrivastava7]

your a leftie like me! :P

[stefanjoseph900]

why does Sn approach a?

[2logj]

absolutely fantastic

[Lexbell]

Excellent video, I found this very helpful :)

[UMgooch]

awesome review on how to do Taylor series, thanks for posting!

[OpenTheTrollGate]

EXPLAIN WHY IT WORKS

[shamaaz11]

I've learned more from watching your "series" playlist over a weekend than I have from 2 months worth of calculus lectures....you're my saviour!

[LinWilliam]

and this is the reason i couldn't sleep yesterday?!?!! omg patrickjmt ure my math fairy <3

[asdertyu89]

is so easy do the mc laurin series after see this video..thanks..

[TheConfusedKnight]

This video is more popular in Ethiopia than it is anywhere in Europe or Australasia :) Intriguing!

[sirpops92]

I was very lost on this subject matter going into my test but watched these videos the night before and felt very confident. Thank you.

[staceyehurst]

you are my saviour <3

thanks so much for making these videos!

[mitchyisgay]

you say "well" a lot :)

[bluesmanrooffie]

you, sir... are awesome!

[mkamalkayani]

20 people failed their cal test.-_-

[JCLlobet16]

why is a=0?

[sawfell]

@JCLlobet16 He took the series around the number 0. You can also make a=2, a=3, a=3/2. or any real you desire. and then use Taylor series on it and you can then find the series around the number you've chosen.

[hardcoresoft]

Thank you so much for your help! You're the reason I passed Calc 2=)

[buhoman3]

And he uses a sharpie while doing math!! What a badass

[tom505]

Problem:

Find the 9th derivative of e^(x^2) (at a=0) using maclaurin series. I've asked so many people that I know and no one has been able to answer this. Our prof didn't do a good job of explaining. She did, however, give us the answer: 9th derivative of f(0) = 9!/6 = 60480

I think this would be a great example for a video :) Thanks for your help patrick!

[MKD772]

Problem:

Given f(x) = *"Summation sign" Infinity on top and k=0 on the bottom* (sin k/k!) x^k for all x, find a power series expression for

f ' (x), and a power series expressing for F(x)= *integral sign* f (t) dt.

Thank you so much I hope you get this!

[k0nste]

Ohhh thank you soo much!!!

NO ONE else could explain this too me until someone pointed me here. Legend!

[PaoRamirezQ]

You are awesome, thank you so much for helping us! I'm trying to resolve the
 Cos(2x) up to term in X4(the 4 is exp).. :)

[PaoRamirezQ]

You are awesome, thank you so much for helping us!

[Adeodatus229]

Hey, up for some high-energy quantum tunnelling tonight?

[jhorb4]

This is the best video for IB math :D Thanks man

[adamaz3644]

patrick,do you have any video that related with the leibniz rule?

[MetallicAus]

Patrick... U saved me in my last year maths exam, and I'm sure you will save me this year too. thanks a lot

[knt070]

thank you so much!!

[0moooaaath0]

شكرا يا حلو

[Monty1992able]

who pressed dislike button....????

Great man

[Sethraz]

Leftie!

[hawx786]

wow this is amazing, text books always have a harder way to explain things :(

thank you so much, 15 marks for tmrows exam are all thanks to you :D

[hawx786]

wow this is amazing, text books always have a harder way to explain things :(

thank you so much, 15 marks for tmrows exam are all thanks to you :D

[EdSoLe]

i wish you were my professor. mine sucks

[queenroxy93]

Hey I was wondering if you also have videos on Calculus 3??? Cuz your videos saved me when I was taking Cal 2 last semester and im about to take Cal 3 in my next one...

[aerialaces21]

Seriously your the Batman of Calculus to me if i need help youtube it, and you pop up!

[4everPho]

my gosh why didnt i see this vid before my calculus 2 exam im a freshman at college.eheh

[moeinmoein]

(Thank you)!

your videos save my butt.

[DRMRBOY92]

Patrick, I just finished watching your videos in preparation for my calc. 2 final tomorrow. Thank you so much for putting all of these extremely helpful videos up on youtube. I now know I can do well because of you. :D

[omgthatscrazyx]

You make me happy to go to school in the morning : )

[Goldfishhhhhhhhhh]

Hey Patrick!,

Thanks a lot for this video! You've saved my butt quite a few times this semester :D

Cheers

[ModelOrange]

I feel like I can smell your sharpie.

[Jennaferification]

you are a BOSS



[lilypetal91]

Oh my god. You made something which seemed utterly incomprehensible in my textbook into something totally understandable. Thanks a bundle! (:

[BrosephKim]

fuck thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you

[mistajchua]

This guy is a hero to calc students.

Especially withAP Calc BC exam tomorrow

[bluemagenta23]

@soccaplaya3303 me too! in eighteen hours I will have taken the last serious math test of my life (because statistics doesn't count haha). this video helped SO much.

[soccaplaya3303]

I'm taking the Calc BC exam tomorrow and your videos saved my life. They taught me how to do various concepts that I had no clue about in literally five minutes per concept. I don't know how to thank you, but I would just like to say no matter how I do on the test tomorrow, I am truly indebted to you. Thank you so much!

[bigTXnD]

now i ve found a math tutor besides my school one :0)

[aaronhoodrich]

I would say to have my babies, but I am a boy...

[guitarhamster102]

OMG ur a tutor in AUSTIN?

Do you go to UT?

[supershah101]

i am going to name my 4th-born child after you!

[gutwrencher89]

there's something reassuring about watching someone do math with a permanent marker... thanks for the help, great lesson

[13ellzcamp]

Just gotta say that these are awesome. You do a lot better job explaining these than my Calc instructor.

Thanks

[jadi929]

you my friend, are a genius

[dluo117]

You, sir, are amazing. I have to take the AP Calc BC test in less than two weeks, and now I feel slightly less dead thanks to you!

[thehype2142]

excellent video. Thank you so much, U have taught me more in a few days than a $300 textbook has in months

[NateTheGreat555]

Everything just seems so much simpler in these videos. Great help for my calc test tomorrow!

[cookiemonsteronthego]

Calculus 2

Before patrickjmt:

Term Test 1= 32.5 out of 50

After patrickjmt:

Term Test 2 = 50 out of 50

Term Test 3 = 48.5 out of 50

Thanks ma nigga!

[fooochahot]

Brilliant!

[fooochahot]

Brilliant! Much appreciated!

[dylankw]

I like you so much sire that I am going to make you a one time offer, that you cannot refuse. I will trade YOUR knowledge of calculus for MY first born daughter. Yes, that is right. You may have my FIRST BORN DAUGHTER for the meager price of your presumably infinite knowledge of calculus. What do you day?

[Jesuskrieger]

You're the man, Patrick! I wish you'd come teach at Clemson University...

[markiemarkwizinsky]

THANK YOU SO MUCH

[cutay51]

i think im a love. you are amazing.

[idaho777]

you go through a lot of paper

what kind of paper do you use?

[MetalSio]

how did mathematician come up with these formulas seriously!?

Thanks Patrick!

[millenniumf1138]

Wow! You explained in six minutes what took my professor a 50 minute lecture to explain! I've got a calc quiz tomorrow, and this has been very helpful! :D

[Bosskane]

THANK YOU OMG!!! :D

[WowfiedPerson]

thx bro that was very clear and straightforward.

[MichaelKeehls]

this proves that textbooks suck

[ericsayres]

You literally saved me from failing my exam on series. Thanks a ton.

[sanzo21]

hullo patrick!

why is it that in the book, they do f'(0)/1!, f''(0)/2!...the same thing as you are doing, but they are tagging on an extra x? Like instead of f''(0)/2!, they do (f''(0)/2!)x^2? Im confuzzled...thanks for the help!

[rubywolf999]

I LOVE YOU!!! i would probably fail calc without you!

[breannuhh08]

im being dead honest when i say this, if it wasnt for you i would have failed my calculus class. THANK YOU!!!!! :D

[Tampied]

you are amazing

[cutemurmaid]

The video was so helpful, thanks.

btw, I love your handwriting.

[EmceeDG]

Wow thank you so much, I was literally about to tear up trying to understand this before i came across your video. I know you might not know me or anything, but wow your video shows real dedication to teaching, and for that I am truly grateful.

thanks for much!!

[EgoWafflez]

Your videos literally taught me the entire chapter on series. Thanks so much!

[patrickJMT]

@EgoWafflez my pleasure!

[charles00069]

@EgoWafflez me too :)

[CMShockk]

Thanks!

[supperhey]

THANKS A LOT !!!!!! ^^

[mrlnx3]

I love your handwriting.

o_o

[panchod100]

man i was watching one of your videos on the basics of mathematics, but this is brilliant man. :D

[tipoupee2000]

You make this stuff so easy to learn. I missed a couple of classes in my college calculus class and you help tons! Thanks a million :)

[JesusisMyGrandson]

You da best pat.

[stoweawy]

Calculus test tomorrow -_________-

[CedeThriftyRuinous]

Has there been a general method devised to reverse a Taylor series?

[CedeThriftyRuinous]

You have to get your name on some mathematical theorem , brilliant video.

[patrickJMT]

@CedeThriftyRuinous not going to happen in this lifetime