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Simple critical point question - how to specify?

  1. Jul 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Classify the critical points subject to the constraints:
    0<=x, y<=Pi

    2. Relevant equations

    fx=sin(y)sin(2x+y)
    fy=sin(x)sin(2y+x)


    3. The attempt at a solution

    Clearly one set of critical points will be (n*Pi,m*Pi) where m <=1 and n and m are all positive and negative integers (Z)
    Another will be where 2x=y and where 2y = x but this is only true where x and y = 0
    Another is where 2x+y = n*Pi and 2y + x = m*Pi

    I think that is it covered however how do I write this in a precise mathematical way?
     
  2. jcsd
  3. Jul 6, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Great!

    Solve this pair of equations for x and y. The solutions, of course, will depend on "mPi" and "nPi" and I suspect (0, 0) will be included in it.

     
    Last edited: Jul 8, 2010
  4. Jul 8, 2010 #3
    Thanks a lot for your replies. So is it enough to simply say:

    y=1/3 Pi(2m-n) where 2m-n<3

    x=1/2 Pi(2n-m) where 2n-m=>0 or 2n=>m

    Is this enough to describe the critical points in a mathematically correct way?
     
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