How to understand Taylor/Mclaurin series?

[Jrohazn]

I'm in Calculus 2, and I have a final coming up. I did extremely well in all other sections, but this section is extremely confusing. I can represent functions into a basic MacLaurin series, and I can also take the derivative of a function and find the series through manipulation of the function into 1/1-x and take the integral of that. Taylor series, though, is EXTREMELY confusing. I have no idea what to do, and no matter how hard I try, I can't find the pattern. Please help!

 

[scottdave]

I'm not sure which part you are stuck on. Sometimes it just helps to read a different text on the subject. MacLauren series are just specialized cases of Taylor series (a = 0), if that helps you. Here is a link to one site that I like. http://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx

I hope it helps.

 

[haruspex]

I'm in Calculus 2, and I have a final coming up. I did extremely well in all other sections, but this section is extremely confusing. I can represent functions into a basic MacLaurin series, and I can also take the derivative of a function and find the series through manipulation of the function into 1/1-x and take the integral of that. Taylor series, though, is EXTREMELY confusing. I have no idea what to do, and no matter how hard I try, I can't find the pattern. Please help!

Maclaurin series are just a special case of Taylor series, expanding the function about the value 0 instead of the more general expansion about a point x=a.
Rather than launch into an explanation of Taylor series from scratch, how about you find a reasonable online explanation and come back here to ask about any parts you don't understand? Paul's online notes are generally very good: http://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx

Edit: well, that's an endorsement - we independently picked the same site.

 

[PeroK]

Another endorsement from me for Paul as a reference for all things calculus.

 

[Kaura]

Khan Academy has a few well put together videos on Taylor Series.

Here are two




Hope this helps and good luck on your final.

 

[MAGNIBORO]

this video also is great

 

[Kaura]

this video also is great

Knowing the quality of 3Blue1Brown's videos I would certainly recommend that OP check that video out.

 

[scottdave]

Yes that is a good video. I will take a look at some of other 3Blue1Brown videos.

 

[yosimba2000]

Taylor series is just saying "can I rewrite a function as an infinite summation of C(x-a)^(increasing powers)".

So say I have the function 2x. Taylor series asks, can 2x be written as C₁(x-a)⁰ + C₂(x-a)¹ +C₃(x-a)² +C₄(x-a)³ + ...

The answer is yes, and you can do it for any function. To show this, you have to find out a method to calculate the constants C.

Here is a great and simple proof of Taylor Series.