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I How to understand Taylor/Mclaurin series?

  1. May 19, 2017 #1
    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!
     
  2. jcsd
  3. May 19, 2017 #2
    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.
     
  4. May 19, 2017 #3

    haruspex

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    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.
     
  5. May 20, 2017 #4

    PeroK

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    Another endorsement from me for Paul as a reference for all things calculus.
     
  6. May 20, 2017 #5
    Khan Academy has a few well put together videos on Taylor Series.

    Here are two




    Hope this helps and good luck on your final.
     
  7. May 20, 2017 #6
    this video also is great
     
  8. May 20, 2017 #7
    Knowing the quality of 3Blue1Brown's videos I would certainly recommend that OP check that video out.
     
  9. May 21, 2017 #8
    Yes that is a good video. I will take a look at some of other 3Blue1Brown videos.
     
  10. May 24, 2017 #9
    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.
     
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