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I'm evaluating a line integral written in the form:

$\int_{\partial\Omega_1} v\nabla u\cdot n$ where $\partial \Omega_1$ is simple curve forming one part of the boundary $\partial\Omega$ of a closed region, and $n$ is the unit normal to $\partial\Omega_1$.

Suppose C(t) is a positively oriented parameterization of $\Omega_1$. Since there is no differential explicitly indicated in the integral, can i automatically assume that the differential is $||C'(t)||dt$?

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    What's the source of this notation? I have not seen it written this way.2012-09-14
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    Its in *Understanding and Implementing the Finite Element Method* by M.S. Gockenbach.2012-09-14
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    Ah, yes I have seen it written that way before, I was misinterpreting it.2012-09-14
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    I believe you can. Compare, for instance, the notation in your book for the divergence theorem and [this notation of the divergence theorem](http://en.wikipedia.org/wiki/Divergence_theorem#Multiple_dimensions). Perhaps someone more familiar with the book will come along with a more definitive answer, however.2012-09-14
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    @MichaelBoratko: Yes, in fact, I'm evaluating the RHS integral in this notation. I'm parameterizing a curve around a quadrilateral, one segment at a time. Would $dS_{1}$ (in my case) be equivalent to ||C'(t)||dt?2012-09-14
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    Again, I'm hesitant to say yes unequivocally because I have not used the notation myself often. That being said, I would think that $dS_1$ would be the same as $ds$ in your [typical line integral notation](http://en.wikipedia.org/wiki/Line_integral#Line_integral_of_a_scalar_field), so yes I believe you are correct.2012-09-14
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    let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/4821/discussion-between-michael-boratko-and-paul)2012-09-14

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