1. Not finding help here? Sign up for a free 30min 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!

Finding the first-order taylor polynomial

  1. Jan 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Basically, I have a differential equation. One of the elements of it is...

    F(P) = 0.2P(1 - (P/10))

    And I need to replace it with it's first-order Taylor polynomial centered at P=10.

    3. The attempt at a solution

    I haven't done Taylor polynomial stuff in over a year so I went and looked it up...as near as I could tell, an FOTP of an equation was the equation plus the derivative of that equation times (x - a). Is this accurate?

    If so, this is fairly simple, as I can find the derivative of F(P) as 0.2 - 0.04P. but what do I do with the (x - a) part? I think for my purposes it would be (x - P), but still, how do I treat this?
  2. jcsd
  3. Jan 21, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You do not take the FOTP of an equation, you take the FOTP of a function. Here the function is F and the variable is P.

    In general, if f is a function and we write x the variable on which it depends, its FOTP at the point a is the function

    [tex]x\mapsto f(a)+f'(a)(x-a)[/tex]

    In your case, f=F, x=P and a=10.

    I leave to you the pleasure of finding the FOTP of F at 10
  4. Jan 21, 2009 #3
    The value a is the point you are expanding around. In your case a = 10. You expand to first order so the differential equation can be solved by analytical methods. Let x = P. Then the equation is

    F(x) = 0.2x(1 - (x/10))

    The first order expansion is then

    [tex]F(x)\approx F(10) + F'(10)(x-10)[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?