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Homework Help: How to rewrite 2D Gaussian eqn in terms of x?

  1. May 21, 2010 #1
    http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png" [Broken]

    How to rewrite this 2D Gaussian eqn in terms of x?
    i need to calculate the x and y values.
    let x0=0 and y0=0.

    is it complex?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 21, 2010 #2

    HallsofIvy

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    Science Advisor

    What do you mean by "write in terms of x"? It is already written in terms of x and y and cannot be written in terms of x only.

    Do you mean "solve for x"? Again, because it is a function of both x and y, you cannot solve it for x alone. You can assume a specific value for y and then solve for x.

    But to "solve for x" you would also have to have a specific value of f(x,y).

    I simply don't understand what you mean by "calculate the x and y values". In general, x and y can have any real values. What conditions are you placing on f(x,y) to give specific x and y values that you could calculate?
     
  4. May 21, 2010 #3
    yes sorry i mean solve for x

    let f(x,y) = y = 2. say
     
  5. May 22, 2010 #4

    Mentallic

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    I've never seen [itex]\sigma[/itex] so assuming it's to be treated as a constant, yes you certainly can solve for x given y and f(x,y). It's relatively simple too.

    [tex]-ln\left(\frac{f(x,y)}{A}\right)=\frac{(x-x_0)^2}{2\sigma_x^2}+\frac{(y-y_0)^2}{2\sigma_y^2}[/tex]

    It should be obvious from here how to solve for x.
     
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