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Math Help - why this expression means all solutions

  1. #1
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    why this expression means all solutions

    http://i45.tinypic.com/140hqtx.jpg

    they say that the integral represents all the solutions for the equation


    i cant understand why???

    as i see it we can multiply our found single solution and multiply it by a constant
    and we get endless variations of our single solution.
    Last edited by transgalactic; December 9th 2009 at 08:19 AM.
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    http://i45.tinypic.com/140hqtx.jpg

    they say that the integral represents all the solutions for the equation


    i cant understand why???

    as i see it we can multiply our found single solution and multiply it by a constant
    and we get endless variations of our single solution.
    Well, this can be attained by A(k), which is any arbitrary (integrable) function of k...

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Well, this can be attained by A(k), which is any arbitrary (integrable) function of k...

    Tonio
    i cant see how it cant be attained by the properties of A(k)

    i dont know whats A(k)
    i dont know why they take the integral

    if i would be asked to find all the varieties of the single solution
    i would just multiply it by constant

    i dont know what they have done there
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  4. #4
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    Quote Originally Posted by transgalactic View Post
    i cant see how it cant be attained by the properties of A(k)

    i dont know whats A(k)
    i dont know why they take the integral

    if i would be asked to find all the varieties of the single solution
    i would just multiply it by constant

    i dont know what they have done there
    ]

    A(k) is ANY complex (integrable) function, so if you want to multiply soem particular solution by s, say, you can as well take sA(k) since A(k) is pretty arbitrary...

    Tonio
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  5. #5
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    ok so A(k) is like multiplying by constant
    it creates a variety of solutions which differ by the multiplication of this function
    depending on the k we put inside



    whats the integral for?

    integral means sum for me
    why they sum all the solutions?

    of course k needs to go from plus infinity till minus infinity

    but why sum all the solutions??
    Last edited by transgalactic; December 9th 2009 at 02:23 PM.
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