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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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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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.

[justinpeterson]

Best explanation of Taylor Series I've seen.

[nadirgg]

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.

[mockingbird]

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!

[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!

[MrMarkgyuro]

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

[julianbeatty]

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

[sumitkumarsahoo]

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

[kelumo]

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

[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

[thefunnyegg-felr]

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.

[randomeggthatworksforthefb]

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

[nehalkalita]

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

[thomasjacques]

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

[gardenmenuuu]

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

[fahdsbahi]

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

[boaozhang]

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!

[alexdotdash]

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

[FabricioRWitt]

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