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
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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...
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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
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Parametric Equations:
• Parametric Equations I...
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Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzread.info/dash/bejne/iGV1raOkd63Sfps.html
@richmondamore8836
2 ай бұрын
🎉
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
5 жыл бұрын
rt
@Sneaky1ne
5 жыл бұрын
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
5 жыл бұрын
3 months ago, hmmm. I'm in the same situation as you. What college do you attend?
@isaacdamon26
3 жыл бұрын
facts
@f4ux578
3 жыл бұрын
why yall learning this in college im in highschool and we have to learn this b u l l s h i t
I owe all of my final grades to this man and adderall
@nikkim8098
6 жыл бұрын
lmfaoo
@nadonkeys0107
5 жыл бұрын
same tho
@shamelessbeauty9658
5 жыл бұрын
I can't cope without him
@benjamintraudcampos2828
5 жыл бұрын
at 1.25 speed cuz adderall lmao
@emilygonzalez2527
5 жыл бұрын
I've never related more to anything in my life
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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
5 жыл бұрын
Oh yeah yeah, understanding math is great.
@HypCarlos
5 жыл бұрын
@@tacosamuel Why does everyone have the Arnold pic? I am confused
@tacosamuel
5 жыл бұрын
@@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
5 жыл бұрын
Oh yeah yeah
@garyzhuang5894
5 жыл бұрын
@@tacosamuel I always thought thats a picture of Postal's Dude
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
3 жыл бұрын
Honestly
@killerking1122
11 ай бұрын
Good ❤
19:12 The Organic Chemistry Tutor breaks character !!!!
@IvoryQirat
3 жыл бұрын
lmaoo he sounded so pissed off
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 KZread. God Bless You, Sir!!!!
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
3 жыл бұрын
Have you seen this kzread.info/dash/bejne/q65sxcdugMvfo6w.html
@SebastianRodriguez-gi8iq
3 жыл бұрын
dale tini paaa
@sammy5576
3 жыл бұрын
Pin this
@syafsyakirhhh8433
2 жыл бұрын
Tqvm
@moviesclub791
2 жыл бұрын
@@sammy5576 love me
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
2 жыл бұрын
Same. That's why I'm here at 2AM prepping for my calc quiz tomorrow at 6:30 PM. :,,,)
@issajoke220
Жыл бұрын
@@lucaskincanyon7393 so did u pass?
@lucaskincanyon7393
Жыл бұрын
@@issajoke220 no I go a 52% Lmaooo
@courageouscuber9278
Жыл бұрын
@Lucas Kincanyon Yeah, if you are watching at 2AM You're basically screwed
i’m watching this video to put myself to sleep and i have accidentally learned things
@josephdoe5195
4 жыл бұрын
WHAT???????
@daniellabinjo6046
4 жыл бұрын
Cuz your subconscious worked on it while you slept lol
I lost it @ 19:13. Him expressing his frustrations other than math and science equations is >>>. Dead XD
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
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
Dude, you're not only AP tutor but an IB tutor as well. God bless this man.
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
Sir I love you with literally every fiber of my being
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.
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!
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. 🙏🏽
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
2 жыл бұрын
How is it so far?? I am also doing first year in CompSci
@MichaelMdlavia
2 жыл бұрын
@@aurumstinger4479 Hectic bro
@zadsand
Жыл бұрын
How is it now bro? now I'm doing the first year in Computer Science
@MichaelMdlavia
Жыл бұрын
@@zadsand I’m a software engineer at Amazon now. Thanks for bringing me back here
@chinyeamprecious
3 ай бұрын
Hello I'm also a computer science student
I find it funny that I come across " The Organic Chemistry Tutor" -- and listen to a "tutor" run circles around calculus instructors on KZread 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.
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
3 жыл бұрын
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
3 жыл бұрын
There's no such thing as A in Calculus
@iqrakhanamansari8670
2 жыл бұрын
Hey...is this 'TAYLOR SERIES' taught in clge or high schl??
@gnerdeek5362
2 жыл бұрын
@@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).
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!
you are the best. 30 minutes of this is better than 2 hours of my actual class
can't be skipping ads cuz this man has been carrying my carrier.
@iqrakhanamansari8670
2 жыл бұрын
Hey is this 'TAYLOR SERIES' taught in high schl or clge in the US??
@Arnie3
Ай бұрын
@@iqrakhanamansari8670both depending on your level of math
Thanks for taking into consideration every little details. You made me understand Taylor and Maclaurin Series very well.
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!
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.
this covers everything about the calculation of Tylor series! Amazing!
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.
I'm able to work on my homework not by reading the prescribed textbook but by watching these videos. Thank you so much!
holy cow dude i have a calc test tomorrow and you just saved my life. you are a true genius thank you so much
Once again the Organic Chemistry Tutor has come through!
This is my entire assignment sir. I can never thank you enough
you know what................ you are the best thank you so much i now get the simplicity of this unit!!!!!!!!!!!!!!!!!!!!
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
2 жыл бұрын
Gee, calc 3 factorial? What is that even about?
@default3623
Жыл бұрын
@@HanOnkel Lmao😐
@ulasdevrim7492
Жыл бұрын
@@HanOnkel calc6, the ultimate calc
Thank you so much! Didn't expect to understand Taylor and Maclaurin series this easily...
Literally the most instructive math lesson I have EVER been given IN MY LIFE. Thank you so much
You’re a fantastic teacher. Thank you for doing what you do.
whoever is making these videos, bless you man
i would not pass this degree without you! an absolute gem
WOW...You are an amazing tutor!!. God richly bless you
Your lesson it's simple, easy to understand. Thank you so much.
An incredible coverage of the Taylor and Maclaurin series. Great work
YOU are the king of tutoring, thanks!
You just removed the frustration I had with this topic. Now I can smile. Thank you.
Thank you so much for making this, I think this will help me pass my quiz
I hope you are living a blessed, happy life. Thank you for this!
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.
this is perfect. watching your videos has helped me so much in university calculus!!!!!
Great help. Really appreciate the knowledge supplemented by the excellent, didactic written steps.
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thanks so much for explaining this properly! You saved me before my final exam!
You are amazing man. Please dont stop blessing us with knowledge
Thank you so much! Your videos really help me fill in the holes I missed in calculus originally.
@rajendramisir3530
5 жыл бұрын
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
4 жыл бұрын
Nice
My calc final is later on today, thank you so much literally you are the only actual teacher I have
Thank you so much for this, lecture makes zero sense but I don't have to worry when I have these videos!
Thank you for your help! Your channel and videos helps a lot!
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.
God bless you Organic Chemistry Tutor. God bless you.
Just hearing this man's voice assures me that I will be ok for my class, thank you so much!
You are a legend on your own ....I was like dreaming in class but when I opened the utube ....I found a lengend
This guy is the GOAT! He deserves way more subscribers !
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!
this is so thorough and easy to follow, thank you!
man you deserve Heaven because you're serving AND saving the universe.
online school has been so tough for me you're literally the reason i'm passing calc rn ily
You're the light shining every dark corners of the depart!!
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.
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!
your way of teaching is really understandable sir. Thank you very much.
@zukauddin5327
5 жыл бұрын
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
The 91 dislikes are from our professors :)
@sam-kx3ty
4 жыл бұрын
🤣🤣🤣
@stephenmiti8829
2 жыл бұрын
🤣🤣🤣🤣🤣🤣😂😂😂😂
Passed my calculus thanks to this man.
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.
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!
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
You are the only reason I have been passing my physics and calc classes. Many thanks. You down with OCT yeah you know me!
Thank You for helping me for my exams.
thank you very much! very helpful, studying at 2am for the tomorrow exam.. tired of reading the text so your video really helped
I am in love with mathematics and you are great at teaching it my friend.
Man you freaking amaze me.
Watching this on my train ride to school before a quiz, thank you thank you thank you
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
Ай бұрын
Where u at now
This video is just pure mathematic gold! I
Best explanation ever of calculus
sir, thank you very much that video was helpful.
Hello, I'm from Brazil, thank you so much! Help me a lot
I understand Taylor and Maclaurin series thanks to you
You and Professor Leonard are amazing.
Excellent explanation
AWESOME AWESOME TEACHING ............. BLESSINGS FROM INDIA GUJARAT ................. 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
You're the best! Thank you.
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
I have an exam in 30minutes and I just learnt this for the first time..
@sam-kx3ty
4 жыл бұрын
I hope you still passed well ? 👍🏾
If I get a 5 on my Calc AP I'm donating 50
@anonyash
Ай бұрын
Update?
@steak3864
Ай бұрын
@@anonyash Got a 5, also donated
@freestyle3208
Ай бұрын
Love the honesty!
@anonyash
Ай бұрын
@@steak3864 gg my guy. What are you doing now ? Like which degree
@steak3864
Ай бұрын
@@anonyash Math!
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!
thank you so much, this helped me so much.
your video got me to understand the concept more in 10 minutes than my university could in 2 hours. I FUCKING LOVE YOU, MAN.
all i can do to appriciate your video just not skip the ads