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Homework Help: Partial Taylor Series Expansion

  1. Jul 12, 2010 #1
    "Partial" Taylor Series Expansion

    It has been awhile since I have had to use a Taylor series expansion (from scratch). I looked it up on wiki and the rules are easy enough, I am just a little confused as to how I apply it to a multivariable function, but only expand it about one variable.

    For example, if I want to expand the function f(x,y) about x = a only, for let's say the first two terms of the expansion, how would I do that?

    Would it just be:

    [tex] f(x,y) = f(a,y) + \frac{f_x(a,y)}{1!}(x - a)[/tex] ?

    I have a feeling it is not this simple...
    Thoughts?
     
  2. jcsd
  3. Jul 12, 2010 #2

    Hurkyl

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    Re: "Partial" Taylor Series Expansion

    That looks right. The function gy defined by
    gy(x) = f(x,y)​
    is an ordinary single-variable function, and the ordinary Taylor series formula works.
     
  4. Jul 12, 2010 #3
    Re: "Partial" Taylor Series Expansion

    Sweet! Thanks Hurkyl. :smile:
     
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