Intro to Taylor Series: Approximations on Steroids

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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[@ConceptualCalculus]

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.

[@mrcookies409]

So meta

[@devooko]

a meta teacher

[@justinpeterson7643]

Best explanation of Taylor Series I've seen.

[@Frosty-tr3ow]

You should also check out 3blue1brown's video on Taylor series

[@nikobaka5272]

@@Frosty-tr3ow both are pretty good in there one way

[@ravijangrax]

@@Frosty-tr3ow "zackstar" has also made a video on this topic and that one is great 🔥

[@nadirgg5612]

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.

[@mockingbird5919]

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!

[@ogreeni]

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!

[@MrMarkgyuro]

amazing. study math on my own and with your help i m starting to realise we have no limits..

[@sumitkumarsahoo7601]

best teacher I have ever seen, I wish if I could give you a great salute, and a big thumbs up

[@kelumo7981]

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

[@MurshidIslam]

I hope your students appreciate how lucky they are to have you as their teacher.

[@thomasjacques6942]

Was struggling with the idea of a series being ‘centred’ at a certain point, this video made it click, thank you

[@nehalkalita]

So far, the best demonstration of Taylor Series on KZbin. Thank you sir for the detailed explanation.

[@randomeggthatworksforthefb7172]

Whenever I'm confused about an advanced concept in math, I always come straight to your videos.

[@fahdsbahi9888]

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

[@Aiantaschr]

I seriously wonder why can't professors at unis and schools be as inspiring as you are? I have been trying to understand taylor series and your video has helped me to start understanding it

[@gardenmenuuu]

That 10 second intro was lit..best thing I have seen on any math video ever ..Thanks

[@Emma-eq8pm]

Thank you so much! I'm a current Calc 2 student at an engineering school. I tried so hard in class to get this topic, and your video has finally helped me get it! The feeling of relief from getting this is such a great one! Thank you so much for making it make sense! :)

[@mehularora1813]

This is by far the best explanation I've come across!

[@DrTrefor]

Glad it was helpful!

[@amandawhite1701]

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!!!

[@yaboi1525]

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. 🙏

[@FabricioRWitt]

Very good explanation, Dr. Bazett. Thank you, and salutations from southern Brazil!

[@julianbeatty2909]

This might hands down be the best explanation of Taylor series I've seen in my 10 years of studying math.

[@boaozhang7188]

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!

[@Proudmuslimah123]

Its 4 years after you made this video and I am here for the first time. Very beneficial, Thank you 🙂

[@aliasraonic]

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

[@DrTrefor]

Glad you enjoyed it!

[@alexdotdash7731]

What a great video. Very clear explanation, you’re the best!

[@ryanhlavaty3680]

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.

[@kishanvishwakarma3027]

Bro that was the best explanation on the Taylor series on KZbin 😮🛐💗

[@curiash]

It's a must watch video for undergraduates.

[@sumitkumarsahoo7601]

really really awesome your lectures are making maths more and more interesting for me, thank you a lot, greetings from India

[@thefunnyegg-fe8lr]

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.

[@onlyonecjb001]

Brilliant video Dr TB.

[@ahmedwesam7286]

Thank you so much!! Your student from Egypt ♥️

[@jibranhussain6067]

What a great way of explanation

[@learn_Persian_with_bestie]

It was awesome special vectors which change by your explanation and the way you explain about derivatives👌

[@DrTrefor]

Thanks a lot 😊

[@ivanwong4243]

Incredibly clear, with great visuals. I don't even sub to most math channels but you know what, this isn't most math channels :)

[@quanle9133]

Man! You are epic , professor. Brief , clear and deep!

[@continnum_radhe-radhe]

Thank you so much sir for this wonderful video🙏🙏🙏...

[@introversion8705]

this is crystal clear explanation.. OMG! you're so amazing and very inspiring! please continue what you are doing! God bless

[@jamesadeniyi1144]

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.

[@2NormalHuman]

this is the best video about taylor approximation. thank you very much!

[@tomatrix7525]

I really like your video structure. I think the conceptual aspect is more important for starters than pure calculations. Back when I first learnt this we were just given the formula and told that it works.....This was not teaching but just blatant memorisation, which is not really what math is about in essence but rather fundamental understanding imo. Thanks for the great stuff as always on here

[@ayooluwakolawole]

I think you are hands down the best maths teacher on youtube

[@abdullahe3674]

that was... really really good bless you Dr Bazett this quality content is underated

[@DrTrefor]

Glad you enjoyed it!

[@shifagoyal8221]

It hits the idea for the derivation of Taylor series.

[@shyamdas6231]

Thank you ,Sir. I was looking for a video which demonstrated the proof.

[@sri279]

Thanks a lot ...maths should be explanation like this...

[@mohammedosmangoronty]

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

[@rratedmotorcyclerides]

I really liked your method of explaining, well worth subscribing

[@richis2fast4u]

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!

[@quant-prep2843]

this guy is a god sent

[@minorlogic]

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.

[@omerhassan5543]

Thanks a ton Dr Trefor

[@atanumondal9980]

You are that hero professor of my dream ❤

[@DeepRohin]

This is amazing!!! Prolly the only video on youtube which I could easily understand!!!

[@ujjwalyadav6189]

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 🔥🔥

[@ahaditab6364]

Please continue with this teaching .....I am really interested with your teaching

[@mdelgado436]

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?

[@jancyvijico1432]

Wonderful explanation. Excellent

[@theeccentric7263]

Gonna have to watch this a couple times. 😅 Although your explanations are very clear and engaging.

[@q_science]

Buddy, you are the best explainer 👍

[@isitjeevan]

Really wonderful explanation.Thank you sir

[@rogerhoefel8515]

Very clear. Suggestion: I could talk about infinite Taylor Polynomials and more details of approximation errors!

[@theaimwinsbr9874]

Great Information!💖

[@continnum_radhe-radhe]

Sir ,is taylor series of multivariable uploaded on your channel??

[@DrTrefor]

Not yet sorry, but it is a good topic!

[@JoseFerreira-de7oe]

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

[@DrTrefor]

Absolutely! There is a multicariable Taylor formula too

[@JoseFerreira-de7oe]

@@DrTrefor oh wow really?! Wouldn't that be kind of difficult to wrap our mind around it?

[@tewodrosgirma3019]

you are simply amazing.

[@brandonwootton5575]

this is beautiful, how the hell do you even think to come up with something such as this?

[@urpapi6969]

thank you for sharing your knowledge

[@patroyalCH2002]

Taylor series has to be the math's one of the greatest inventions

[@jagpreetsingh6059]

Best explanation.

[@bigseekersb]

Sweet graphics. Very helpful.

[@DrTrefor]

Glad you like them!

[@izgit]

You are a life saver... That's all I can say

[@DrTrefor]

Glad it helped!

[@kutraleeshwaranb2595]

better explanation 👍

[@ravijangrax]

Thank you ❤️ For Such a great explaination 🙏🏼

[@murphp151]

this is v good. Nice work

[@mehransarmadi9157]

finally i understand taylor series , thank you so muchhhhhhhhhhhhhhhhhhhhhh ❤❤❤

[@souravshome8104]

nice explanation

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hello what does on steroids mean, sorry for the question, great video!

[@sangjinlee6412]

Amazing!!.. certainly helpful

[@isaachester8475]

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?

[@supposexy]

Just Great!! WaoW!

[@physicsrmr2949]

Sir,What is the need for derivatives here?how to imagine this,practically in physics

[@hackercop]

Very good thanks

[@roaakanaan9459]

man you are AMAZING!!

[@slomojohnjoshi5990]

Thank you so much, sir 🙏🙏🙏

[@DrTrefor]

Most welcome!

[@damadorian]

one great video! thank you very much !

[@shahidmeir7379]

great work

[@mondsuchtig3533]

Liked for the title!

[@ireneolayinka6517]

absolute icon.

[@a.nelprober4971]

The king of kings

[@shazullahyusufzai5704]

When a=o the graphs pass (0,1) when a>0 where is the location of that point

[@dsflkvbndflvkndflomvpsdmvlkasd]

Great Video

[@AlleEsor28]

AMAZING. This helped me so much, THANK YOUUUU

[@filiplanger7564]

best fu***ing explanation I've seen so far....thx for effort ;)

[@hrperformance]

9:28 it states that mod(x)

[@nehalkalita]

Radius

[@JQuint_]

THIS IS GOLD!

[@JaesNSC]

Very clear and concice

[@DrTrefor]

Thank you!

[@Dan-kg2lm]

That's inspiring

[@user-np5cp4rj9q]

Thanks But what's the difference between taylor series and newton method of interpolation ?

[@DrTrefor]

Newton is only doing the first derivative, taylor can be much more powerful as you can use higher derivatives. But more time costly.

[@darlene506]

Thank you 👊🏾 🇿🇦