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Taylor expansion for f(x,y) about (x0,y0) ?

  1. Apr 23, 2012 #1
    Can someone please explain the Taylor expansion for f(x,y) about (x0,y0) ?

    Would really appreciate some sort of step by step answer :)

    thankyou
     
  2. jcsd
  3. Apr 23, 2012 #2

    hunt_mat

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    Simple, just take a Taylor expansion in [itex]x[/itex] around [itex]x_{0}[/itex]
    [tex]
    f(x_{0}+h_{x},y_{0}+h_{y})=f(x_{0},y_{0}+h_{y})+h_{x} \partial_{x}f(x_{0},y_{0}+h_{y})+h_{x}^{2}\partial_{x}^{2}f(x_{0},y_{0}+h_{y})+\cdots
    [/tex]
    Then take the Tavlor expansion in [itex]y[/itex] of each term. Simple but tedious.
     
    Last edited: Apr 23, 2012
  4. Apr 23, 2012 #3
    Thanks for the reply, it looks logical but I'm stuck on how it all comes together/
    and where does the h^2(x) term in the 3rd term on the right come from
     
  5. Apr 23, 2012 #4

    hunt_mat

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    I am applying the 1D Taylor expansion to the x-variable. I am assuming, you know about the 1D Taylor expansion right?
     
  6. Apr 23, 2012 #5
    yes I do using this equation, f(x) = f(x0) + f '(x0)/1! (x-x0) ...
     
  7. Apr 23, 2012 #6

    hunt_mat

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    The notation I am using:
    [tex]
    h_{x}=x-x_{0}
    [/tex]
     
  8. Apr 23, 2012 #7
    ok, I think i get it, bit slow atm! thankyou!
     
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