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Math Help - Deduction with Stoke's Theorem

  1. #1
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    Deduction with Stoke's Theorem

    Hi guys! I hope someone here will be able to help me with this question:

    f(r) is a scalar field, then use stoke's theorem (∫∫c curlF.dS=∫cF.dr) to deduce that:

    ∫∫s grad(f) x dS = -∫c f dr


    I am stuck as to how to do this. I have tried subbing in the vector calculus identity curl(fu)=fcurl(u)+(gradf)xu (where u is a constant). Thus

    ∫∫s grad(f) x dS = ∫∫s curl(fu) - fcurl(u) (where dS is u)

    but I am not sure whether this is right (and i then get stuck at this point too). Please help!
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  2. #2
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    If u is a constant vector then curl u= 0. But then you say "where dS= u" which makes no sense- dS isn't constant except on planes.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    If u is a constant vector then curl u= 0. But then you say "where dS= u" which makes no sense- dS isn't constant except on planes.
    Yes, I figured out as much. But what would be the first step in the right direction? I am really not sure of what to do.
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  4. #4
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    Sorry, I mean to say: what other vector calculus identity can I could use to solve this problem?
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  5. #5
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    Quote Originally Posted by TheFirstOrder View Post
    Sorry, I mean to say: what other vector calculus identity can I could use to solve this problem?
    I notice that you have started a second thread for this question- you really shouldn't do that.
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    I notice that you have started a second thread for this question- you really shouldn't do that.
    Sorry, I don't quite understand. This question got moved from differential equations because I placed it there by accident, but I began only one thread for this question.

    Sorry again. I didn't realise someone else had started a thread about this question. Do I have to ask a question on that thread now?
    Last edited by TheFirstOrder; May 16th 2010 at 02:55 AM. Reason: oops
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  7. #7
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    My apology! I didn't realize that two different people were asking exactly the same question! Perhaps you and silverflow are taking the same course?
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  8. #8
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    Quote Originally Posted by HallsofIvy View Post
    My apology! I didn't realize that two different people were asking exactly the same question! Perhaps you and silverflow are taking the same course?

    haha. we must be!
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