这个曲面积分，不是同一个向量场。
OK, and that surface integral, well, it's not for the same vector field.
对于曲面积分，也已经知道如何计算。
每当做通量的曲面积分时，你要做两件事。
Whenever you do a surface integral for flux you have two parts of the story.
也就是最终要摆脱曲面积分，回到常规的二重积分。
And this is finally where I have left the world of surface integrals to go back to a usual double integral.
计算这个曲面积分的方法，和其他任何曲面积分的一样。
And, the way in which you would compute the surface integral is just as with any surface integral.
给出曲面积分在空间坐标的正交变换下的一个计算公式。
A calculating formula for surface integrals under orthogonal transformation of space coordinates is given.
这把一个向量场的线积分，和另外一个向量场的曲面积分联系起来。
This relates a line integral for one field to a surface integral from another field.
它建立了有向曲面上的曲面积分与它的边界曲线积分的关系。
It gives a relationship between a surface integral over an oriented surface and a line integral along a simple closed curve.
文章把这些方法推广到曲线积分和曲面积分中，并给出了证明。
This article popularizes these methods in the calculation of curvilinear integral and surface integral and gives proof of them as well.
给出第二型曲面积分计算的几种方法，并举例说明了这几种方法的应用。
In this paper, we give a few methods for calculating second-kind surface integral and their applications.
对曲面积分中值定理，给出了一个新的证明，并举出相关例子加以应用。
In this paper, a new proving of the mean value theorem of integral on surface is given, with some application in related cases presented.
如果在这个曲面积分中是以dx,dy,dz结尾的，则表明出现了很大的问题。
If you end up with a dx, dy, dz in the surface integral, something is seriously wrong.
水利行业经常要进行流量计算，这样就会遇到曲面拟合和曲面积分的问题。
The calculation of flow is often needed in water conservancy, and surface-fitting and double integration are usually met in order to solve this problem.
告诫学生使用高斯公式计算曲面积分时一定不能忽视条件，否则可能导致错误。
It reminds the learners to notice the formula premise when using Gauss Formula, to avoid obtain a wrong result.
在我花了这么多时间来告诉你们，如何计算曲面积分之后，我打算告诉你们，如何避免计算它们。
After spending a lot of time telling you how to compute surface integrals, now I am going to try to tell you how to avoid computing them.
为了理解(5.9.22)中其余那些曲面积分的意义，我们首先考察对应于偶源的解。
To understand the meaning of the remaining surface integrals in (5. 9. 22) we first investigate the solution corresponding to a doublet source.
本文探讨了对称性在第二类曲线积分和第二类曲面积分中的应用，给出了一些有用的结论，并举例说明。
On the base of these notions, the second mean valued theorems for the second type curve integral are proved.
入口截面不消耗剪切功率，然后用上界定理与曲面积分方法首次得到了用余弦模拉拔方棒时变形力的解析解。
Then with the upper-bound theorem and the surface integral an analytical solution of the drawing stress was first obtained.
平面中的通量和空间中的通量有很大区别，在平面中，通量仅仅是线积分的另一种形式，而在空间中，它表现为曲面积分。
Flux looks quite different in the plane and in space because, in the plane, it is just another kind of line integral, while in space it is a surface integral.
本文建立了一种特殊的第一型曲面积分与第一型曲线积分的转化公式，并通过实例表明该方法在解决问题时所带来的方便。
This paper gives the conversion formula from the first type surface integral to the first type curvilineal, and sets a example of using the method to solve exercises.
本文建立了一种特殊的第一型曲面积分与第一型曲线积分的转化公式，并通过实例表明该方法在解决问题时所带来的方便。
This paper gives the conversion formula from the first type surface integral to the first type curvilineal, and sets a example of using the method to solve exercises.
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