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!

Linear Approximation

  1. Jan 18, 2006 #1
    My book gives a formula for linear approximation of two independent variables, but I needed one for three. So I modified the formula given in the book, but I need someone to please just quickly see if it looks okay.

    [tex]f(x,y)=z=f(x_0,y_0)+(\frac{\partial f}{\partial x} (x_0,y_0)) (x-x_0) + (\frac{\partial f}{\partial y} (x_0,y_0)) (y-y_0)[/tex]

    [tex]f(x,y,z)=f(x_0,y_0,z_0)+(\frac{\partial f}{\partial x} (x_0,y_0,z_0)) (x-x_0) + (\frac{\partial f}{\partial y} (x_0,y_0,z_0)) (y-y_0)+(\frac{\partial f}{\partial z} (x_0,y_0,z_0)) (z-z_0)[/tex]

    Does this look alright?
    It looks fine to me but I'm prone to overlooking glaring errors :grumpy:
  2. jcsd
  3. Jan 18, 2006 #2


    User Avatar
    Homework Helper

  4. Jan 18, 2006 #3
    thanks a lot.
  5. Jan 18, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    When you have time, you might want to see if you can rigorously justify that expression!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Linear Approximation
  1. Linear approximation (Replies: 4)

  2. Linear approximation (Replies: 1)

  3. Linear Approximation (Replies: 4)

  4. Linear Approximations (Replies: 3)