# 2018-06-04

Solution. We’ll use Stokes’ Theorem. To do this, we need to think of an oriented surface Swhose (oriented) boundary is C (that is, we need to think of a surface Sand orient it so that the given orientation of Cmatches). Then, Stokes’ Theorem says that Z C F~d~r= ZZ S curlF~dS~. Let’s compute curlF~ rst.

moved from Stokes' theorem as per discussion on that page.. Spelling. This seems to have been argued over for many years, but at least our spelling in the article should match the title. Few people think that Archimedes' principle needs another s, but most people write Charles's law.The problem is that different people use different pronunciations, and so disagree on the correct spelling. Stokes theorem says that ∫F·dr = ∬curl (F)·n ds. If you think about fluid in 3D space, it could be swirling in any direction, the curl (F) is a vector that points in the direction of the AXIS OF ROTATION of the swirling fluid.

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Similarly, Stokes Theorem is useful when the aim is to determine the line integral around a closed curve without resorting to a direct calculation. As Sal discusses in his video, Green's theorem is a special case of Stokes Theorem. 2012-06-18 We’ll use Stokes’ Theorem. To do this, we need to think of an oriented surface Swhose (oriented) boundary is C (that is, we need to think of a surface Sand orient it so that the given orientation of Cmatches). Then, Stokes’ Theorem says that Z Understanding when you can use Stokes.

## Conceptual understanding of why the curl of a vector field along a surface would relate to the line integral around the surface's boundaryWatch the next less

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### Davis, CA 95616. a visual representation of stoke's theorem If you like video explainations, the MIT opencourseware and Khan academy may be of help.

Introduction to Bayes' Theorem Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Similarly, Stokes Theorem is useful when the aim is to determine the line integral around a closed curve without resorting to a direct calculation. As Sal discusses in his video, Green's theorem is a special case of Stokes Theorem.

Video - 12:12: First of 11 videos on Stoke's Theorem: Back to top. Online Math Lab Home: Feedback
To define the orientation for Green's theorem, this was sufficient. We simply insisted that you orient the curve $\dlc$ in the counterclockwise fashion.

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Few people think that Archimedes' principle needs another s, but most people write Charles's law.The problem is that different people use different pronunciations, and so disagree on the correct spelling. Stokes theorem says that ∫F·dr = ∬curl (F)·n ds. If you think about fluid in 3D space, it could be swirling in any direction, the curl (F) is a vector that points in the direction of the AXIS OF ROTATION of the swirling fluid. curl (F)·n picks out the curl who's axis of rotation is normal/perpendicular to the surface.

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### Stokes' theorem intuition | Multivariable Calculus | Khan Academy · Khan Academy Uploaded 7 years ago 2012-06-18. Conceptual understanding of why the

Stokes theorem says that ∫F·dr = ∬curl (F)·n ds. If you think about fluid in 3D space, it could be swirling in any direction, the curl (F) is a vector that points in the direction of the AXIS OF ROTATION of the swirling fluid. curl (F)·n picks out the curl who's axis of rotation is normal/perpendicular to the surface. Stokes' theorem is the 3D version of Green's theorem.

## 2018-06-04 · Here is a set of practice problems to accompany the Stokes' Theorem section of the Surface Integrals chapter of the notes for Paul Dawkins Calculus III course at Lamar University.

The left-hand side surface integral can be seen as adding up all the little bits of fluid rotation on the surface itself. Let's now attempt to apply Stokes' theorem And so over here we have this little diagram, and we have this path that we're calling C, and it's the intersection of the plain Y+Z=2, so that's the plain that kind of slants down like that, its the intersection of that plain and the cylinder, you know I shouldn't even call it a cylinder because if you just have x^2 plus y^2 is equal to one, it would essentially be like a pole, an infinite pole that keeps going up forever and keeps going down Here we cover four different ways to extend the fundamental theorem of calculus to multiple dimensions. Green's theorem and the 2D divergence theorem do this for two dimensions, then we crank it up to three dimensions with Stokes' theorem and the (3D) divergence theorem.

Green's theorem and the 2D divergence theorem do this for two dimensions, then we crank it up to three dimensions with Stokes' theorem and the (3D) divergence theorem. Conditions for stokes theorem. Stokes example part 1. Stokes example part 2.