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Math Help - least action principle

  1. #1
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    least action principle

    let f(x) be a diffrentiable function .if f(0)=0,f(1)=1,then the minimum value of $\int_{0}^{1}( f'(x))^2dx$
    some one give me following hint
    Hint: Integrate by parts:

    \int_0^1 (f'(x))^2\,\mathrm{d}x=\left.f(x)f'(x)\right\vert_  0^1-\int_0^1f(x)f''(x)\,\mathrm{d}x
    Or equivalently, recall principle of least action/energy.[/quote]
    sir i never heard about this principal .can you tell us how can we solve this question with the help of least action principal
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  2. #2
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    Re: least action principle

    The "principal if least action" is a physics principle not a mathematics principle.

    What you talking about is the "Calculus of Variations" but I note that, according to Wikipedia, Calculus of variations can be used to prove the "principle of least action"- under reasonable physical assumptions: Principle of least action - Wikipedia, the free encyclopedia
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  3. #3
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    Re: least action principle

    Quote Originally Posted by HallsofIvy View Post
    The "principal if least action" is a physics principle not a mathematics principle.

    What you talking about is the "Calculus of Variations" but I note that, according to Wikipedia, Calculus of variations can be used to prove the "principle of least action"- under reasonable physical assumptions: Principle of least action - Wikipedia, the free encyclopedia
    sir see the reply of outmeasure sir (2nd reply).i don,t know what he wants to say
    S.O.S. Mathematics CyberBoard • View topic - integration
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  4. #4
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    Re: least action principle

    Quote Originally Posted by ayushdadhwal View Post
    sir see the reply of outmeasure sir (2nd reply).i don,t know what he wants to say
    S.O.S. Mathematics CyberBoard • View topic - integration
    any view
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  5. #5
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    Re: least action principle

    Quote Originally Posted by ayushdadhwal View Post
    any view
    can some body put light on this principle
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