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

[@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.

[@MurshidIslam]

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

[@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!

[@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!

[@MrMarkgyuro]

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

[@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. 🙏

[@sumitkumarsahoo7601]

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

[@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

[@gardenmenuuu]

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

[@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

[@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!!!

[@nehalkalita]

So far, the best demonstration of Taylor Series on UA-cam. 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.

[@thomasjacques6942]

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

[@alexdotdash7731]

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

[@FabricioRWitt]

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

[@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.

[@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! :)

[@quanle9133]

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

[@introversion8705]

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

[@julianbeatty2909]

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

[@Proudmuslimah123]

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

[@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 :)

[@onlyonecjb001]

Brilliant video Dr TB.

[@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

[@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.

[@sumitkumarsahoo7601]

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

[@2NormalHuman]

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

[@raymondho2405]

I really liked your method of explaining, well worth subscribing

[@jibranhussain6067]

What a great way of explanation

[@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!

[@ahaditab6364]

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

[@mohammedosman6549]

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

[@jancyvijico1432]

Wonderful explanation. Excellent

[@isitjeevan]

Really wonderful explanation.Thank you sir

[@mehularora1813]

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

[@DrTrefor]

Glad it was helpful!

[@ahmedwesam7286]

Thank you so much!!
Your student from Egypt ♥️

[@shyamdas6231]

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

[@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!

[@continnum6540]

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

[@ravijangrax]

Thank you ❤️ For Such a great explaination 🙏🏼

[@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 🔥🔥

[@q_science]

Buddy, you are the best explainer 👍

[@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!

[@omerhassan5543]

Thanks a ton Dr Trefor

[@AlleEsor28]

AMAZING. This helped me so much, THANK YOUUUU

[@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 😊

[@sangjinlee6412]

Amazing!!.. certainly helpful

[@ayooluwakolawole]

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

[@theaimwinsbr9874]

Great Information!💖

[@curiash]

It's a must watch video for undergraduates.

[@jagpreetsingh6059]

Best explanation.

[@sri279]

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

[@ctrlw__7-years-ago]

Amazing video, thank you so much!

[@rogerhoefel8515]

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

[@tewodrosgirma3019]

you are simply amazing.

[@theeccentric7263]

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

[@murphp151]

this is v good.
Nice work

[@atanumondal9980]

You are that hero professor of my dream ❤

[@shifagoyal8221]

It hits the idea for the derivation of Taylor series.

[@abdullahe3674]

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

[@DrTrefor]

Glad you enjoyed it!

[@roaakanaan9459]

man you are AMAZING!!

[@mehransarmadi9157]

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

[@JQuint_]

THIS IS GOLD!

[@zed8970]

awesome video. You deserve more views.

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great work

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this guy is a god sent

[@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?

[@dsflkvbndflvkndflomvpsdmvlkasd]

Great Video

[@bigseekersb]

Sweet graphics. Very helpful.

[@DrTrefor]

Glad you like them!

[@filiplanger7564]

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

[@hackercop]

Very good thanks

[@souravshome8104]

nice explanation

[@be.on_teach7415]

Great explanation. Thank you

[@DrTrefor]

Glad it was helpful!

[@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.

[@slomojohnjoshi5990]

Thank you so much, sir 🙏🙏🙏

[@DrTrefor]

Most welcome!

[@chiomaudoh3154]

Lol, u had a whole lot to still say, the video is awesome ✨✨

[@nurazilayahaya]

tq sir....really helpful

[@andrewchen861]

thx this actually makes sense

[@alanliang9538]

good stuff sir

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better explanation 👍

[@izgit]

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

[@DrTrefor]

Glad it helped!

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

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Just Great!!
WaoW!

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Thank you

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thank you!

[@naeem5071]

you are very very good

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absolute icon.

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Very good video!

[@DrTrefor]

Thank you very much!

[@amirhosseindehestani3313]

That was helpful, Thx

[@michellasakuraschoolsimula4039]

Great👍

[@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.

[@nexesdz3907]

nice vid.thanks a lot

[@astha_yadav]

Finally i get it thanks ~ ✿

[@darlene506]

Thank you 👊🏾 🇿🇦

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

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Youre amazing bro

[@DrTrefor]

Thank you!

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a great vedio!