Taylor Series and Maclaurin Series - Calculus 2

This calculus 2 video tutorial explains how to find the Taylor series and the Maclaurin series of a function using a simple formula. It explains how to derive the power series of composite functions using known Maclaurin series of elementary functions.
Full-Length Math & Science Videos:
/ collections
___________________________________
Series Tests - Practice Problems:
• Calculus 2 - Geometric...
Taylor & Maclaurin Polynomials:
• Taylor Polynomials & M...
Taylor's Remainder Theorem:
• Taylor's Remainder The...
Power Series - Interval Convergence:
• Power Series - Finding...
Power Series - Derivatives & Integrals:
• Power Series - Differe...
___________________________________
Power Series - Function Representation:
• Power Series - Represe...
Finding The Power Series:
• Finding Power Series B...
Power Series - Representation By Integration:
• Power Series Represent...
Power Series - Representation By Natural Logs:
• Power Series Represent...
Taylor & Maclaurin Series:
• Taylor Series and Macl...
Binomial Series:
• Binomial Series
____________________________________
Parametric Equations:
• Parametric Equations I...
Calculus Final Exam and Video Playlists:
www.video-tuto...

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/jGKkfHShfK-fhJo

[@richmondamore8836]

🎉

[@ericplz7420]

Sir, you deserve my college tuition, my college doesn't deserve a single penny when all they do is write a fricking textbook on the chalkboard and expect to know everything. Thank you for every single thorough explanation and giving many examples so that I can understand.

[@monicagarza1761]

rt

[@Sneaky1ne]

part of being a good student is also learning for yourself by looking for proper sources, such as this one, but be certain that a true understanding of the matter is not achieved by watching this video alone, although it does bring us a long long way ahead of just the school lectures. Also, exposure in class combined with these videos is much more effective than just the videos. Make no mistake this guy also maybe saved my finals

[@tacosamuel]

3 months ago, hmmm. I'm in the same situation as you. What college do you attend?

[@isaacdamon26]

facts

[@f4ux578]

why yall learning this in college im in highschool and we have to learn this b u l l s h i t

[@coenvanbeelen3746]

So i have a calculus test tomorrow and no professor has ever made me undestand this. I watched this video and it's completely clear. You're worth you weight in gold man

[@tacosamuel]

Oh yeah yeah, understanding math is great.

[@HypCarlos]

@@tacosamuel Why does everyone have the Arnold pic? I am confused

[@tacosamuel]

@@HypCarlos a youtuber named Maximilianmus told his subscribers to switch their profile pictures and spam comment sections. It has since ended, but some people still have them on.

[@brandondunn6838]

Oh yeah yeah

[@garyzhuang5894]

@@tacosamuel I always thought thats a picture of Postal's Dude

[@averyrobinson4666]

Every single time I'm faced with an adversity, and I've become stranded in the waning hours of the night. One man has always been there to rescue the damsel in distress. One man has found a way to save me countless times before I knew I even needed to be saved. ONE MAN is always there waiting. The Organic Chemistry Tutor Thank you

[@considerthelilies48]

Epic

[@physicsisawesome696]

Damn!

[@ebadrahman1290]

mf glazing out here

[@sarahvincent6144]

Thank you for explaining a week of my calc class in 30 mins and helping me pass my finals. You are a true hero.

[@eduardomoreira7624]

Honestly

[@killerking1122]

Good ❤

[@dysmaruuramsyd3233]

I didn't have even the slightest bit of intuitive understanding of Taylor Series expansion from 3 hours of reading my textbook. This one single video explained the entire concept perfectly. You're an absolute lifesaver man.

[@lucaskincanyon7393]

Same. That's why I'm here at 2AM prepping for my calc quiz tomorrow at 6:30 PM. :,,,)

[@issajoke220]

@@lucaskincanyon7393 so did u pass?

[@lucaskincanyon7393]

@@issajoke220 no I go a 52% Lmaooo

[@EliteCubingAlliance]

​@Lucas Kincanyon Yeah, if you are watching at 2AM You're basically screwed

[@khalidjamal3848]

19:12 The Organic Chemistry Tutor breaks character !!!!

[@DaniyalX]

lmaoo he sounded so pissed off

[@akueijohnsonateny]

I just took 15 minutes of my life just to understand what really makes you the best tutor of all time, and one thing I discovered is that you assume the learners know absolutely nothing. This is what it means to be a perfect teacher; to know that people might not know what you know. You explain every piece of your work, including what makes the difference between 2 and 1 equals 1. Because of you, I don't go to Math class frequently because I know there's a better class on KZbin. God Bless You, Sir!!!!

[@smorris5296]

I owe all of my final grades to this man and adderall

[@nikkim8098]

lmfaoo

[@nadonkeys0107]

same tho

[@shamelessbeauty9658]

I can't cope without him

[@benjamintraudcampos2828]

at 1.25 speed cuz adderall lmao

[@emilygonzalez2527]

I've never related more to anything in my life

[@kxngmar2748]

0:00 Taylor series for function f(x)=ln(x) centered at a=1 7:14 Taylor series for function f(x)=e^x centered at a=3 10:49 Maclaurin series for function f(x)=sin(x) 17:05 Maclaurin series for cos(x) using Maclaurin series for sin(x) 23:02 Maclaurin series for cos(x^2) 24:28 Maclaurin series for xcos(x) 25:30 Maclaurin series for function f(x)=x^2 e^(-x) 27:31 Maclaurin series for function f(x)=cos^2x

[@minxiao8434]

Have you seen this kzbin.info/www/bejne/r6ublJhrhc2sqas

[@SebastianRodriguez-gi8iq]

dale tini paaa

[@sammy5576]

Pin this

[@syafsyakirhhh8433]

Tqvm

[@moviesclub791]

@@sammy5576 love me

[@colleenbungard9476]

If nobody got me, I know that organic chemistry tutor got me. Every time I'm stuck, lo and behold, this white knight has posted a clear, detailed explanation that trumps that of every textbook I've ever touched. I would die for you good sir. You are worth more than gold.

[@nolapickering1917]

My AP calc test is in 3 days. This is the first time I've thoroughly understood this topic. You, sir, are a god next to the American education system

[@tyscott4949]

I find it funny that I come across " The Organic Chemistry Tutor" -- and listen to a "tutor" run circles around calculus instructors on KZbin and in the classroom teaching calculus II. I have spent about an two hours or so taking notes reading reference calculus books and digesting the Taylor Series and at the same time find it soothing that things are becoming clear, what once was amiss, in the midst of the fog. Thank you, I will join the page when I start my calculus class this summer of 2022.

[@vardhanadhikari5510]

Dude, you're not only AP tutor but an IB tutor as well. God bless this man.

[@phantom4902]

Sir, you're a gem, this was the topic I was facing the most difficulty with and you made it look so simple. Thank you for existing

[@lesegomokgabudi5798]

i had no idea on how to solve Taylor series and its younger brother Maclaurin series....but now i have an idea. Thanks a lot my brother

[@GamingWithMicc]

The best of the Best, I've been watching his videos since grade 10. Today I'm doing first Year in Computer science at Wits. Shout out to this man, I'll probably stream his videos in my Phd years.

[@aurumstinger4479]

How is it so far?? I am also doing first year in CompSci

[@GamingWithMicc]

@@aurumstinger4479 Hectic bro

[@zadsand]

How is it now bro? now I'm doing the first year in Computer Science

[@GamingWithMicc]

@@zadsand I’m a software engineer at Amazon now. Thanks for bringing me back here

[@chinyeamprecious]

Hello I'm also a computer science student

[@xb5959]

I've been watching your videos since high school, and now I'm in college taking up Biochemistry and I'm still watching your vids for most of my subjects and it has helped me a lot in ways my professors could not. It's been difficult to learn in classrooms and online classes bc I have inattentive type ADHD but these lecture videos keep me going. Thank you very much for this. I will repay when I finish my degree and land a decent job. I have one suggestion though, which is to have lecture notes from the examples to be available online because it's difficult to take notes from the video, but this is mostly because I'm cramming and I do not have much time to take notes but I need to. Thank you and please continue to do this.

[@HK-ez8vm]

can't be skipping ads cuz this man has been carrying my carrier.

[@iqrakhanamansari8670]

Hey is this 'TAYLOR SERIES' taught in high schl or clge in the US??

[@Arnie3]

@@iqrakhanamansari8670both depending on your level of math

[@vhiedkc859]

My A’s in maths n physics are from you sir not our boring unclear professors. Much love you really deserve my tuition fee & extra pay. Asante sana. 🙏🏽

[@abigailreimer-golden8856]

Dude you are the only reason I passed calc II I swear. I love you so much

[@watertantrums2000]

I lost it @ 19:13. Him expressing his frustrations other than math and science equations is >>>. Dead XD

[@42laar]

wow, i've been taught taylor's series in class, review sessions, recitations, and youtube videos. this explanation is by far the best one at helping me understand it. i feel much more confident about taylor's series now. thanks a lot!

[@Justreemm]

Sir I love you with literally every fiber of my being

[@danielcash1037]

Words don't describe. Thank you very much. In your explanations, you don't do large algebraic simplifications which make it difficult to understand the logical process on the fly and I appreciate that. I'm not sure why every other teacher I've had does it because it is not helpful when learning a new topic. You consistently teach and ensure you go through each explanation thoroughly. You make a good assumption of prior knowledge in your videos and give lots of examples to solidify the learning. I think you're videos are perfect, the best I've seen. Thank you very much.

[@connectingspyyo8159]

i took calc 2 almost 2 years ago and I am super worried about calc 3! Thank you so much for this, as it is a great refresher. I feel like you taught this better than my professor did at the time

[@HanOnkel]

Gee, calc 3 factorial? What is that even about?

[@default3623]

@@HanOnkel Lmao😐

[@ulasdevrim7492]

@@HanOnkel calc6, the ultimate calc

[@xoxo__diana]

I want to thank you so so much! my professor and IA made this series so hard to understand during lecture/discussion, but you made it so easy to understand!

[@thomasblackwell9507]

It has been close to 40 years since I first started using this stuff but it still is amazing to see how much it is worth knowing!

[@chukwumandive9597]

All I can say is WOW!! Thank you so much. You have no idea the amount of knowledge you're dishing out there. I can now boldly flex my new found powers in solving Taylor and Maclaurin series. You are a life saver.

[@jelome_x]

You just removed the frustration I had with this topic. Now I can smile. Thank you.

[@ronak859]

whoever is making these videos, bless you man

[@jacquelinet9109]

i’m watching this video to put myself to sleep and i have accidentally learned things

[@josephdoe5195]

WHAT???????

[@daniellabinjo6046]

Cuz your subconscious worked on it while you slept lol

[@mahyarkharazi1360]

wow thank you so much you always help me in my math classes and i wouldnt know what to do without you. your vidoes have helped me all the way back from grade 9 and now im in first year university. this is the most valuable channel on youtube keep up the good work.

[@shubox]

you are the best. 30 minutes of this is better than 2 hours of my actual class

[@kristineopenshaw6415]

I'm able to work on my homework not by reading the prescribed textbook but by watching these videos. Thank you so much!

[@Alejandro-mo4pt]

This guy is a genius!!! This might be basic calculus , but the way he explain it, is just perfect. He makes it easy

[@incredibleplanet]

my First comment just for this guy to know he is saving lives! READ IF YOU WANNA PASS CALC 2 .........at my college half of the people fail this class and i was sure that i was gonna fail this class taking it over the summer with other class( chem 2) but with you and God i passed it with a B woohoo! with you and God I passed chem 1,2 , Physics, calc 1,2. and taking organic next semister! for people who are strugling, i am truly duuuumb at math and i took it over the summer because i know he has videos. so what i did was study 7 hours a just for calculus 2! and before the exam i study/revewed 25-30 hours so for this class 49 hours a week + 30 hours of review before the exam lol. do what i did and you will pass, i did not care about life until i passed calc 2! i did not wanna take it twice so i worked harrd! THANK YOU my tutor!

[@willpizzo3629]

holy cow dude i have a calc test tomorrow and you just saved my life. you are a true genius thank you so much

[@constance5004]

online school has been so tough for me you're literally the reason i'm passing calc rn ily

[@EnjoimentProductions]

Thank you! The part that helped me most is when you are making the summation notation of the function. Your red notes show what part of the expression is n = 0, n = 1, n = 2, n = 3, n = 4 @ 10:04 . This was so helpful. I could not find any visual in my textbook that showed what part of the expression relates to which n. But you laid it out in red and that helped me make sense of it all. Thank you again!

[@crustyflamingo1023]

Just hearing this man's voice assures me that I will be ok for my class, thank you so much!

[@gboyawesome1159]

This guy is the GOAT! He deserves way more subscribers !

[@sethkirotichdauphin1784]

you know what................ you are the best thank you so much i now get the simplicity of this unit!!!!!!!!!!!!!!!!!!!!

[@V.Z.69]

I remember learning this. I got an 'A' in the class. An 'A' in Calc I, II, and III. Now, I just can't remember why I learned it and I never used it since I graduated.

[@sooners2037]

That happened to me when I was a undergrad barely used calculus until Atmospheric Dynamics decided to retake Calculus1-3 when I went to grad school occasionally I use Calculus but the computers do the calculations it’s good to know depending on the profession

[@berkayustem6344]

There's no such thing as A in Calculus

[@iqrakhanamansari8670]

Hey...is this 'TAYLOR SERIES' taught in clge or high schl??

[@gnerdeek5362]

@@iqrakhanamansari8670 College. I'm pretty sure he meant college undergrad (the first few years of college, required for an associate's degree or bachelor's degree) vs college grad school (college to get a master's degree or doctorate).

[@tejaamathi3039]

I kind of wish that job interviews just conducted exams instead of making us waste our money to go to college to get a degree. I'm not an excellent test taker, but I'd much rather just self-learn and take an exam to get a job plus an interview session, rather than having to spend 40k+ on a degree. This channel just proves how one person can self-learn and be just as competent if not more competent than a person who studied for hours with a textbook. Thanks a million, OCT for helping me understand a topic in just 30min!

[@elaine6060]

this covers everything about the calculation of Tylor series! Amazing!

[@oswilmathematics]

Thanks for taking into consideration every little details. You made me understand Taylor and Maclaurin Series very well.

[@karolinshikam7919]

man you deserve Heaven because you're serving AND saving the universe.

[@gabrielladesch-obi5754]

I have a calc final today and I had no idea what I was doing until rn thank u so incredibly much . When everyone has been sure I’d fail , I’d watch ur videos and turned up with some of the highest grades in the class . You r a life saver if I knew u and could pay you 1000 dollars I would but unfortunately I’m a poor student

[@bobsandwich3431]

Where u at now

[@terrancepage9163]

I'm at a point in my class where the textbook is zero help. I have no idea what its talking about anymore. This, however, is saving me and getting me through the class. Thank you so much!!!!

[@terrancepage9163]

11 months later and I still have the same philosophy. Taking Differential Equations now and brushing up on my series knowledge. This is the video that just keeps on giving. You're a legend!

[@adnanhowlader143]

while university taking my dad's hard working money and provides low level teaching , and you are sir doing god's work

[@ethanwelling4546]

Just remember why you're doing this man. To get a goddamn piece of paper

[@alisonalexander9057]

Once again the Organic Chemistry Tutor has come through!

[@alejandroill]

Literally the most instructive math lesson I have EVER been given IN MY LIFE. Thank you so much

[@natashasthilaire1950]

My calc final is later on today, thank you so much literally you are the only actual teacher I have

[@danerasmussen2062]

I like how you always bring it back to that larger formula =, and you parse out what the series will be from there. It makes it very repeatable.

[@wtfooqs]

your video got me to understand the concept more in 10 minutes than my university could in 2 hours. I FUCKING LOVE YOU, MAN.

[@alpharibo]

Watching this on my train ride to school before a quiz, thank you thank you thank you

[@zettabyte212]

i would not pass this degree without you! an absolute gem

[@jeremygalloway1348]

Sir...you provide an immeasurable value to mathies everywhere. Of all creed, sex, sexual preference, race,and of all math levels. Those of us who are about to take our finals...SALUTE YOU!

[@mwabakombe1238]

You are a legend on your own ....I was like dreaming in class but when I opened the utube ....I found a lengend

[@biscuitquack9152]

This is my entire assignment sir. I can never thank you enough

[@3467AAA]

Why are you the only one who goes straight to the point and explain it as quick and as substantially clear as you do? Why do the other channels feel like giving you their biography, the biography of who created the theorem, that he was sitting on his school classroom and the light of divine came to him and put images of functions and equations in his head... blah blah gosh!

[@thomasyeboah1860]

😂

[@ningurp281]

I never did precalculus or calculus 1 and I understood this , wow... I didn't know what a factorial was and it is so fun..

[@Mai-ml7lb]

ngl, i might be cooked.

[@thatboy_deedee]

i think i am

[@sharpy2016]

It's the dang Limaçons for me

[@camillebokiba9625]

We in this tg🥲

[@Blank19111]

So cooked🥲

[@dayoyusuf7180]

Same here gang😅, I’ll give an update on how the exam goes later on

[@minhquangly8100]

Pay thoundsand of dollar and still going to this chanel for study. You desevered my tuition

[@endarkened5153]

It took me only 7 minutes to understand taylor and maclaurin series after watching 1 of your examples. Before that, I was scratching my head for 1 hour in class wondering what my professor was doing to get the taylor/maclaurin series.

[@hannahdo980]

Thank you so much! Didn't expect to understand Taylor and Maclaurin series this easily...

[@alifarhat8072]

I stopped going to the sessions and prefer to go get my attendance in and leave class. Professor is useless, this is priceless!

[@homierdawg]

God bless you Organic Chemistry Tutor. God bless you.

[@danimanabat5791]

I hope you are living a blessed, happy life. Thank you for this!

[@randomthinkingindividual]

thank you very much! very helpful, studying at 2am for the tomorrow exam.. tired of reading the text so your video really helped

[@ciiil8802]

Passed my calculus thanks to this man.

[@sandilemtambomalibongwe9477]

You're the light shining every dark corners of the depart!!

[@areebakhan5738]

this is perfect. watching your videos has helped me so much in university calculus!!!!!

[@Onesmo]

I have an exam in 30minutes and I just learnt this for the first time..

[@sam-kx3ty]

I hope you still passed well ? 👍🏾

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for explaining the difference between Taylor and Maclaurin Series in Calculus Two. The two names that are most commonly associated with Power Series are Brook Taylor and Colin Maclaurin. Elementary and Transcendental Functions can be represented as Taylor/Maclaurin Series. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@poggom]

what is this AI comment

[@fatmacdacat]

You are the only reason I have been passing my physics and calc classes. Many thanks. You down with OCT yeah you know me!

[@emmafox7022]

Thank you so much! Your videos really help me fill in the holes I missed in calculus originally.

[@rajendramisir3530]

Same here Emma. JG's majestic explanations and working through a variety of questions have excited my interest in Infinite Series. Utube was not there when I struggled with this topic. I didn't quite learned Combinatorics when I studied it. I am preparing to start the BS in applied and computational mathematics. We ought to support and subcribe to JG's Utube channel.

[@almaktoumsajwani723]

Nice

[@bluestone1017]

Sometimes i wish i could do your class face to face, you've been saving me, thankyou

[@danytoumie1319]

YOU are the king of tutoring, thanks!

[@ArjunSinghBhadauriya]

Thank You for helping me for my exams.

[@Peter_1986]

I literally watched this entire playlist from start to finish.

[@whoisdanielsong]

An incredible coverage of the Taylor and Maclaurin series. Great work

[@tsadiamabel]

Well done Sir. You are really a genius in Maths. All your explanations that I have watch are super-awesome. They are just so so so great. Words can't describe it. God bless you.

[@aarieffawwaz7984]

I HAVE A CALCLUS FINAL IN ABOUT 3 HOURS, I HOPE I PASS THIS COURSE. THANKYOUUU FOR THE EXPLANATION

[@Trußþÿ_cŕuizè]

Your work will be used forever!

[@suhartiwijayanti1719]

all i can do to appriciate your video just not skip the ads

[@aidengonzalez8073]

Thank you so much for this, lecture makes zero sense but I don't have to worry when I have these videos!

[@nirmalupadhyay4548]

AWESOME AWESOME TEACHING ............. BLESSINGS FROM INDIA GUJARAT ................. 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

[@celsiusfahrenheit1176]

I don't care what people say, you are very intelligent

[@themichaelcom]

I really love your videos. I believe I got a 4.0 in chemistry because of you. Also because of my hard work, but you made it easier for me to achieve it. Thank you.

[@Himawari_.]

your way of teaching is really understandable sir. Thank you very much.

[@zukauddin5327]

That was awesome, it has just cleared all the doubts I had regarding to single variable. I just want to ask that what if there will be two variables in the function

[@krischris6165]

Thanks so much for doing this, God bless u!!! I always come to your channel for breakdown, u are the best YT for this, saving lives

[@rigelstar8037]

I am in love with mathematics and you are great at teaching it my friend.

[@swahilibrian7860]

If I could pay you i would...your methods are simple and easy to understand

[@ΓιώργοςΜάριοςΜερκούρης]

This video is just pure mathematic gold! I

[@abdulfattahyassin1722]

You're genius man Is there anything you don't know?😂 Thanks a lot for making my life easier ❤️❤️

[@qudusadewale1263]

You are amazing man. Please dont stop blessing us with knowledge

[@matthewcroy7704]

Thank you so much bro you explain it so well for me, it's harder for me to understand it when my professor is lecturing

[@minhvu8682]

Your lesson it's simple, easy to understand. Thank you so much.