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March 27th, 2018, 11:22 PM   #1
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what is Stokes’s theorem?

hello
what is application of Stokes’s theorem?
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March 27th, 2018, 11:54 PM   #2
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Please stop these threads with one line questions. I don't mind if you post them, but I really doubt that you're learning anything useful here. Please tell us what math and physics you do know, why you want to know about Stokes and what you already know about Stokes.
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March 28th, 2018, 02:44 AM   #3
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i know nothing about stokres i want to learn it.
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March 28th, 2018, 03:43 AM   #4
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Math Focus: Yet to find out.
Maybe focus on odd an even numbers first...
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March 28th, 2018, 04:24 AM   #5
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Quote:
Originally Posted by integration View Post
i know nothing about stokres i want to learn it.
Sure nice, you want to learn Stokes. You don't tell me why or what you know, so I have limited information. But get any multivariable calculus book and work through it. You'll get to Stokes at the end.
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March 28th, 2018, 04:31 AM   #6
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First, Stoke' theorem has nothing to do with 'Linear Algebra'. You can, however, find it in any Calculus text. In it's most general form it is a generalization of the fundamental theorem of Calculus- it says that $\displaystyle \int_{\partial \Omega} \omega= \int_\Omega d\omega$.

Here $\displaystyle \Omega$ is some n-dimensional differentiable manifold and $\displaystyle \partial \Omega$ is its n-1 dimensional boundary; $\displaystyle \omega$ is an n-1 dimensional differential form and $\displaystyle d\omega$ is its differential.

In one dimension, $\displaystyle \Omega$ is, say, the interval [a, b] and $\displaystyle \partial \Omega$ is its boundary, the two points a, and b. $\displaystyle \omega$ is some function of one variable, f(x), and $\displaystyle d\omega$ is its differential, dx. In those terms, Stoke's theorem says that $\displaystyle \int_a^b df= f(b)- f(a)$, the "Fundamental Theorem of Calculus".

"Stoke's Theorem" in two dimensions is called, in most Calculus texts, "Green's theorem" $\displaystyle \oint_C \left(Ldx+ Mdy\right)$$\displaystyle = \int_D \left(\frac{\partial M}{\partial x}+ \frac{\partial L}{\partial y}\right) dxdy$.

The form most often given as "Stoke's Theorem" in Calculus texts is three dimensional: $\displaystyle \int_\Gamma F\cdot d\Gamma= \int_S \nabla\times F \cdot dS$.

Now, does any of that make sense to you? Have you taken a Calculus class? I get the impression, from what you have said that you are a young person, with a good healthy curiosity, who comes across these words in reading but have not taken much mathematics classes. You have to understand that all of these things involve deep background knowledge. You are welcome to ask questions but please let us know where you ran acros these words and what you do understand about them so we will know what kind of explanations will make sense to you.
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March 28th, 2018, 05:00 AM   #7
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Thanks Country Boy, that Alabama Approach is particularly clear (mathematically).

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