Intro to Taylor Series: Approximations on Steroids
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- While in Calc I we used Linear Approximations, can we approximate functions by quadratics, cubics, etc? Indeed, Taylor Series (and Maclauren series when they are centered at x=0) provide a method for effective approximation of functions locally. And the best part is all we need to know is a lot of information about derivatives all at one point, and this is enough to get, typically, a decent approximation locally.
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When I want a high-quality vid with good graphics that emphasizes concepts over mechanics, I check your channel first. You are the math teacher's math teacher.
So meta
a meta teacher
What’s special about your vids, is that you’re not just trying to show us how to solve a question for a math test. You’re educating people from all over the world to truly understand the concept and reasoning between these seemingly abstract topics. Thank you so much!
This video really made me appreciate Taylor series, as my professor didn't do much besides showing us the general formula. Thank you so much!
Dr Trefor you are a superstar!!I finished my engineering degree a while back,I just happen upon your videos and was captured by your passionate presentation,very good graphics and concise explanations...I'm just going through your videos just for fun and to remind myself of some concepts I had already forgotten
Whenever I'm confused about an advanced concept in math, I always come straight to your videos.
Was struggling with the idea of a series being ‘centred’ at a certain point, this video made it click, thank you
So far, the best demonstration of Taylor Series on TH-cam. Thank you sir for the detailed explanation.
really great video here. it has all the pretty graphics which make sense, but unlike the other pretty graphics videos, it still has a solid explanation. thanks for this, sir
Glad you enjoyed it!
I am very grateful to the way, how you explain Taylor Approximation. I have seen many videos in different languages but yours is the best
Best explanation of Taylor Series I've seen.
You should also check out 3blue1brown's video on Taylor series
@@Frosty-tr3ow both are pretty good in there one way
@@Frosty-tr3ow "zackstar" has also made a video on this topic and that one is great 🔥
This video is elegantly made with such a good quality. And it is Easy to understand! I found this very helpful! Thank you for your help and passion!
Thank you good Sir,
This is the first time I have really understood Taylor Series this semester, and right on time too seeing as my final is on Monday! Love the clarity and the why, not just the how. You've saved me twice this year!!!
I think you are hands down the best maths teacher on youtube
really really awesome your lectures are making maths more and more interesting for me, thank you a lot, greetings from India
This is amazing!!!
Prolly the only video on youtube which I could easily understand!!!
Physics is not just about solving problems by putting the given values in an equation, it is also about the core or kick of the topics ur studying 👍🏼🔥. Btw I was wandering from yesterday to get a proper explanation on Taylor's series and found this 🔥🔥
What a great way of explanation
Thank you so much sir for this wonderful video🙏🙏🙏...
Thanks a ton Dr Trefor
Thank you so much!!
Your student from Egypt ♥️
Gonna have to watch this a couple times. 😅 Although your explanations are very clear and engaging.
Buddy, you are the best explainer 👍
You are that hero professor of my dream ❤
Really wonderful explanation.Thank you sir
you are simply amazing.
The king of kings
Hello. Quick question, can be Taylor Series be represented as "composition" of simpler polynomials? If yes , than better numeric stability and order faster calculation. Thanks.
better explanation 👍
Thank you 👊🏾 🇿🇦
You are a life saver... That's all I can say
Glad it helped!
Great Information!💖
one great video! thank you very much !
AMAZING. This helped me so much, THANK YOUUUU
Sweet graphics. Very helpful.
Glad you like them!
thx this actually makes sense
thank you!
this shit brazy...... love it
Sir how to express the any series of real number in a xy plane
Amazing video, thank you so much!
Taylors theorem on two variables ???
Indeed there is such a theorem and is quite important, but I don't have a video on it just yet!
@@DrTrefor would you make it for us sir...!!!
Great explanation. Thank you
Glad it was helpful!
you are very very good
Thanks
But what's the difference between taylor series and newton method of interpolation ?
Newton is only doing the first derivative, taylor can be much more powerful as you can use higher derivatives. But more time costly.
thats nuts!
In the beginning was the Word, and the Word was with God, and the Word was God. 2He was with God in the beginning. 3Through him all things were made; without him nothing was made that has been made. (John 1:1-3)
💯
😍
Slow your talking speed pls
This is the best explanation of Taylor Series on the internet, because you have explained the core of it rather than directly explaining the steps on how to work with it.
❤️
I hope your students appreciate how lucky they are to have you as their teacher.
amazing. study math on my own and with your help i m starting to realise we have no limits..
best teacher I have ever seen, I wish if I could give you a great salute, and a big thumbs up
What a great video. Very clear explanation, you’re the best!
this is beautiful, how the hell do you even think to come up with something such as this?
Very good explanation, Dr. Bazett. Thank you, and salutations from southern Brazil!
I’m not joking, I’m currently watching this video in the middle of my math class about Taylor series because my professor is doing a terrible job of explaining it compared to you. Thank you so much!!! I’m understanding this concept for the first time now.
Sir ,is taylor series of multivariable uploaded on your channel??
Not yet sorry, but it is a good topic!
best fu***ing explanation I've seen so far....thx for effort ;)
Great👍
Liked for the title!
Thank you ,Sir. I was looking for a video which demonstrated the proof.
Very good thanks
Dr Trefor Bazett - This video is very much helpful. Thanks so much.
But I want to ask.
Is it possible to use Taylor's series model to increase a rate?
I'm a petroleum engineering student, I don't know if a model can be developed from Taylor's Expansion model for the increase of oil production rate.
That 10 second intro was lit..best thing I have seen on any math video ever ..Thanks
That's inspiring
I really liked your method of explaining, well worth subscribing
Just Great!!
WaoW!
this is v good.
Nice work
that was...
really really good
bless you Dr Bazett
this quality content is underated
Glad you enjoyed it!
mind blown
this guy is a god sent
nice explanation
holy shit ur good
I did that 1k
Thank you ❤️ For Such a great explaination 🙏🏼
It was awesome special vectors which change by your explanation and the way you explain about derivatives👌
Thanks a lot 😊
Man! You are epic , professor. Brief , clear and deep!
This might hands down be the best explanation of Taylor series I've seen in my 10 years of studying math.
When I took math, caculus 2, they didn't have much time to talk about Taylor's theorem. That's because these classes are taught in 9 weeks and meeting 2 times per week. Absolutely horrible for an average student.
This is by far the best explanation I've come across!
Glad it was helpful!
Youre amazing bro
Thank you!
THIS IS GOLD!
An excellent video (as usual) by Dr. Bazett. My questions around Taylor Series have always been some form of the following: I either know calculus or don't know calculus. If I know calculus, why do I need an approximation? I know the function and can compute the function and its derivative at any point. If I don't know calculus, how can I calculate the Taylor series which requires knowing first, second and n-derivatives of the function?
Thank you! Every resource, be it textbook or video, tells you how to do a Taylor series, but this is the first time I've seen the "why" of a Taylor series.
The last week of calc 2, we were supposed to learn Taylor Series. I was struggling mightily in the class. I made the choice to totally punt that content and focus on the rest of the course material to prep for the final exam. Technically my strategy worked, as I passed the class. But I have carried guilt over never actually learning Taylor Series at all.
This video at least gave me the basics to now know what I missed. Thanks for that!
Just can't appreciate you enough for putting such great effort and time to produce quality content one after another. You make things seem so easy to understand no matter the complexity. You're one of the best teacher I've ever came across. 🙏
thanks a lot, this video was very useful for me . although I watched some videos to understand the Taylor expansion, this one was the best
this is crystal clear explanation.. OMG! you're so amazing and very inspiring! please continue what you are doing! God bless
Very clear. Suggestion: I could talk about infinite Taylor Polynomials and more details of approximation errors!
Now the real question is: Can we take this concept and apply it to multivariable calculus? Oh and btw best explanation I've seen so far
Absolutely! There is a multicariable Taylor formula too
@@DrTrefor oh wow really?! Wouldn't that be kind of difficult to wrap our mind around it?
Just like someone standing away from the board and reading a script fast while waving his arms. Never tries to explain how Taylor came up with his Polynomial.
So no explanation of WHY the Taylor polynomial is a power series of X. Why not some other series and why the progressive differentiation etc. Just directions re how to use it.
Thanks a lot ...maths should be explanation like this...
It hits the idea for the derivation of Taylor series.
Best explanation.
Amazing!!.. certainly helpful
It's a must watch video for undergraduates.
Taylor series has to be the math's one of the greatest inventions
Why do you add all of the higher orders together? Why not just replace each previous order terms with the higher order term each time?
Too complicated explanations for simple concept