Results 1 to 2 of 2

Math Help - Positively Homogenous Function (Euler's Theorem)

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    144

    Question Positively Homogenous Function (Euler's Theorem)

    For the function,

     u(x,y) = x^{2}f(\frac{y}{x})

    determine whether the following statement is true or false,

    x\frac{\partial{u}}{\partial{x}} + y\frac{\partial{u}}{\partial{y}} = 2u

    Now I realize this can be quickly checked by the use of the chain rule, but isn't there an easier way to verify this since one can see that the statement we are being asked to check is in fact a positively homogenous function of degree 2?

    It's almost identical to the statement for Euler's Theorem in my textbook, but I don't fully understand how this will help our current situation.

    Would someone care to explain?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2010
    Posts
    144
    Bump, still need some explaination.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: January 10th 2011, 08:51 AM
  2. Homogenous function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 10th 2009, 07:55 AM
  3. Euler's Theorem and Function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 6th 2009, 10:47 AM
  4. Euler's Phi Function and Chinese Remainder Theorem
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: June 2nd 2008, 04:52 PM
  5. euler function and theorem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 30th 2007, 11:59 AM

Search Tags


/mathhelpforum @mathhelpforum