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March 27th, 2018, 11:22 PM  #1 
Senior Member Joined: Nov 2017 From: india Posts: 188 Thanks: 1  what is Stokes’s theorem?
hello what is application of Stokes’s theorem? 
March 27th, 2018, 11:54 PM  #2 
Senior Member Joined: Oct 2009 Posts: 350 Thanks: 112 
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.

March 28th, 2018, 02:44 AM  #3 
Senior Member Joined: Nov 2017 From: india Posts: 188 Thanks: 1 
i know nothing about stokres i want to learn it.

March 28th, 2018, 03:43 AM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,577 Thanks: 536 Math Focus: Yet to find out. 
Maybe focus on odd an even numbers first...

March 28th, 2018, 04:24 AM  #5 
Senior Member Joined: Oct 2009 Posts: 350 Thanks: 112  
March 28th, 2018, 04:31 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,089 Thanks: 846 
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 ndimensional differentiable manifold and $\displaystyle \partial \Omega$ is its n1 dimensional boundary; $\displaystyle \omega$ is an n1 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. 
March 28th, 2018, 05:00 AM  #7 
Senior Member Joined: Jun 2015 From: England Posts: 795 Thanks: 233 
Thanks Country Boy, that Alabama Approach is particularly clear (mathematically). 

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