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!

Simple Taylor expansion

  1. Sep 14, 2008 #1
    1. The problem statement, all variables and given/known data

    What is the quadratic approximation to the potential function?

    2. Relevant equations

    U(x) = U0((a/x)+(x/a))
    U0= 20

    3. The attempt at a solution

    This is just the last part of a question on my engineering homework, I never learned Taylor expansions before even though I have taken all the class prerequisites. So if you could just walk me through it that would be much appreciated.
  2. jcsd
  3. Sep 14, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Read this http://en.wikipedia.org/wiki/Taylor_series and try it out yourself. It's just a cookbook formula. You have to add various derivatives of U(x) at x=4 times powers of (x-4) up to quadratic. It's not that mysterious. We'll be glad to look at your efforts.
  4. Sep 14, 2008 #3
    So for my first try I got U=(1.25)x2-10x+60. I am pretty sure I remember something about only going out to the second order place to make it "quadratic" so I got.

    40 for the first place, 0 zero for the first order, and 1.25x2-10x+20 for the second order.

    Does this look right?
  5. Sep 14, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    Yes, that's right. For most purposes you probably want to leave that in the form 40+5*(x-4)^2/4, since you are thinking of x's near 4.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Simple Taylor expansion Date
What went wrong with my simple differential equation? Jan 19, 2018
Simple integration to find area Nov 21, 2017
Simple Taylor series Sep 3, 2013
Taylors series for simple ODE Jul 16, 2012