Stokes' theorem

So, if we really wanted to apply Stokes theorem, because I've been telling you that space is simply connected, and I will always be able to apply Stokes theorem to any curve, what would I do?

因为我已经告诉过你们空间是单连通的，所以，如果我们真的想要运用Stokes定理，那么我总是可以把它运用于任何曲线，我应该做什么呢？

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Based on the Stokes theorem and the boundary element theory, the basic equation of the radiation angle factors and the mutual radiation area for calculating radiation heat transfer was deduced.

运用Stokes公式及边界元理论，导出了辐射换热计算中的辐射角系数与相互辐射面积的计算基本公式。

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So, food for thought: let's say that I want to apply Stokes theorem to simplify a line integral along the curve here.

大家想一想：，假定我想利用Stokes定理，来简化这么一条曲线上的线积分。

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The rotational flux due to the rotating frame can be calculated exactly for each cell face using the Stokes theorem.

由于坐标系旋转引入的旋转通量能由网格单元面上Stokes定理精确得出。

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The accurate formulae which express component and total magnetic anomalies of uniformly-magnetized polyhedron by using angular coordinate and magnetic parameters are derived from coordinate-turning conversion, Gauss 'divergence theorem and Stokes' theorem.

文中采用坐标旋转变换、应用Gauss散度定理及Stokes定理，建立了用角点坐标和磁性参数值表示的均匀磁化多面体磁异常各分量及总磁异常的精确表达式。

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But for that, I needed to be able to find a surface which to apply Stokes theorem.

但是对于这个，我需要找到一个可以运用Stokes定理的曲面。

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Based on testifying the integrand divergence free property of the traction boundary integral equation and Stokes' theorem, the computation of traction boundary integral equation can be transformed into the evaluation of the displacement potential function on the boundary points.

证明面力边界积分方程被积函数的散度等于零，应用Stokes公式，对平面线弹性问题，将面力边界积分的求解转化为边界点的位移势函数的点值计算。

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And, let's say that I want to apply Stokes theorem.

如果我想要运用Stokes定理。

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Well, the orientation I should have for Stokes theorem is that Well, if you look at the convention around here, it tells us that the normal vector should be going this way.

对于Stokes定理中的定向&，观察这里，它的法向量应该是这个方向。

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So, I'm going to say a couple of words about surface independence in Stokes theorem.

我将讲述一些，关于Stokes定理的曲面独立性。

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So, now that tells us we can actually apply Stokes theorem, except it won't fit here.

这告诉我们可以运用Stokes定理，这里写不开了。

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Well, the strategy, I mean there are other ways, but the least painful strategy at this point is to observe what we already know is a special case of Stokes's theorem.

策略是。。。，还有其它方法的，但是此时最好的方法就是，利用已经知道的特殊情况。

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Well, to be able to use Stokes theorem, I need, actually, to find a surface to apply it to.

为了能够应用Stokes定理，我需要找一个曲面来应用它。

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We have a connection between that, which is Stokes theorem.

还有一种联系的方式就是Stokes定理。

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OK, one last thing I want to show you before we start reviewing, so one question you might have about Stokes theorem is, how come we can choose whatever surface we want?

在开始复习之前，我想讲点东西，大家对Stokes定理可能有一个疑问，我们如何选择我们想要的曲面？

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