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Homework Help: Calculating errors in Functions of two variables Taylor Series

  1. May 31, 2010 #1
    1. The problem statement, all variables and given/known data
    From the taylor series we can replace [tex]x =x_{0} + h[/tex]
    but how does
    [tex]\delta f = f(x_{0} + h, y_{0} + k) - f(x_{0},y_{0})[/tex]
    become
    [tex]\delta f = hf(x_{0}, y_{0}) + kf(x_{0}, y_{0})[/tex]
    I can see the first step, but how do you get it to the second?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 31, 2010 #2

    Mark44

    Staff: Mentor

    [tex]\Delta f(x, y) = f(x_{0} + h, y_{0} + k) - f(x_{0},y_{0})[/tex]
    [tex]\approx f(x_{0}, y_{0}) + f_x(x_0, y_0)\Delta x + f_y(x_0, y_0)\Delta y - f(x_{0},y_{0})[/tex]

    In the Taylor expansion above, terms of order 2 and higher are omitted.
     
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