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Math Help - Solving Lınear Equations with Inequality Costraints

  1. #1
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    Solving Lınear Equations with Inequality Costraints

    Hi people,

    Do you know a good source that reviews this topic in detail.

    Thanks in advance.
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  2. #2
    Member Haven's Avatar
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    The subject in question is known as Linear Programming/Optimization

    I recommend Linear Programming and it's Applications by James K. Strayer. It covers the simplex algorithm which is the by far the simplest algorithm for solving such systems. Give you a great introduction to the field, along with Tableaus.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Mr. Haven... I think you have a mistake in your signature!

    e!=Gamma(e+1)
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    thanks for your sincere help, people.
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    And Mr. Haven... where is i?

    I think you should pass the i...
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  6. #6
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    Not only that, you can't write e! anyway, since the factorial function is only defined for positive integers. So e! \neq \Gamma(e+1).
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  7. #7
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    Strictly speaking you are correct, but since the \Gamma(n+1) =  n! for n \in \mathbb{N} . It's useful to use the gamma function to define the factorial function for non-integer reals.

    I.e, \frac{1}{2}! = \frac{\sqrt{\pi}}{2}

    So it is merely an extension of the factorial function. Many sources agree with me on this point.
    Last edited by Haven; July 11th 2010 at 02:27 AM.
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  8. #8
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    Quote Originally Posted by Haven View Post
    Strictly speaking you are correct, but since the \Gamma(n+1) =  n! for n \in \mathbb{N} . It's useful to use the gamma function to define the factorial function for non-integer reals.

    I.e, \frac{1}{2}! = \frac{\sqrt{\pi}}{2}

    So it is merely an extension of the factorial function. Many sources agree with me on this point.
    Yes I agree with you as well. In fact, generalising the factorial function was the whole purpose of creating the Gamma function. But that doesn't mean that writing the factorial of anything but a nonnegative integer isn't garbage...
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