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: Basis functions for polynomial

  1. Sep 10, 2010 #1
    1. The problem statement, all variables and given/known data
    For I = [a,b], define: P3(I) = {v: v is a polynomial of degree ≤ 3 on I, i.e., v has the form v(x) = a3x3 + a2x2 + a1x + a0}. How to show v is uniquely determined by v(a), v'(a), v(b), v'(b).


    2. Relevant equations



    3. The attempt at a solution

    I'm not exactly sure what I'm being asked to do here. I don't need the problem solved, just a nudge in the right direction.
     
  2. jcsd
  3. Sep 10, 2010 #2

    epenguin

    User Avatar
    Homework Helper
    Gold Member

    I guess I = [a,b] just stands for an interval of real numbers?

    I also guess that you are allowed to assume that multiplication and addition of given real numbers always produces a unique real number?

    Then your four given coefficients ai uniquely determine P.

    So it seems you are being asked to prove that v(a), v'(a) etc. uniquely determine the ai .
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook