1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook