This relates a line integral for one field to a surface integral from another field.
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。
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.
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。
Use geometry or you need to set up for double integral of a surface.
总之，就是用几何方法或是在曲面上建立二重积分。
Now, how would we actually set up a flux integral on such a surface.
下面应该如何，在这样的曲面上建立通量的积分。
Whenever you do a surface integral for flux you have two parts of the story.
每当做通量的曲面积分时，你要做两件事。
And, the way in which you would compute the surface integral is just as with any surface integral.
计算这个曲面积分的方法，和其他任何曲面积分的一样。
There are two choices. Basically, whenever you want to set up a flux integral you have to choose one side of the surface.
有两种选择，当你要建立通量的积分时,就必须取定曲面的正向。
OK, and that surface integral, well, it's not for the same vector field.
这个曲面积分，不是同一个向量场。
And this is finally where I have left the world of surface integrals to go back to a usual double integral.
也就是最终要摆脱曲面积分，回到常规的二重积分。
Because a surface is a two-dimensional object, that will end up being a double integral.
由于表面是二维的，所以结果是二重积分。
And so it will be a surface integral, not a line integral anymore.
所以要用面积分，而非线积分。
And instead I will want to reduce things to a surface integral.
相反，我想要把它变成面积分。
Double integral of F.dS or F.ndS if you want, and to set this up, of course, I need to use the geometry of the surface depending on what the surface is.
就是做F·dS或是F·ndS的二重积分，为了能建立积分，需要用到曲面的几何性质，这与该曲面的类型有关。
It is a surface integral, so we need to have two variables in there.
它是一个面积分，所以这里需要两个变量。
What it says on each small flat piece — it says that the line integral along say, for example, this curve is equal to the flux of a curl through this tiny piece of surface.
它可以对任一个小平面使用-，比如说对于这条曲线的线积分，等于通过这个曲面的旋度通量。
Mural: Painting applied to and made integral with the surface of a wall or ceiling.
壁画：描绘在建筑物墙壁和天花板上并与其成为一体的绘画。
Considering the influence of the input disturbance, a mathematical description of road surface irregularity is established, which is the model of integral white noise and inspire with sine wave.
同时，考虑到路面扰动输入对悬架控制的重要影响，建立出积分白噪声形式的路面不平度数学模型及正弦激励模型。
Charge is the time integral of current,. Charge is often measured on a quantity of particles, on a surface, or on a component such as a capacitor.
电荷是电流对时间的积分，(公式)电荷常常用一个表面上的带电粒子数，或一个元件(如电容器)上的粒子数来度量。
Integral absolute mean curvature is introduced to describe average curving of an orientable closed surface.
引入积分绝对平均曲率来描述可定向闭曲面的平均弯曲程度。
Based on the wind tunnel test, aerodynamic modal force spectrums of twin-tower tall building are studied using surface integral method of rigid model.
在双塔楼风洞试验基础上，采用刚性模型表面风压积分法对双塔高层建筑气动力谱进行了研究。
The imported advanced Japanese slope surface protection technique-metal frame integral protection technique is introduced in this paper.
较为详细地介绍了引进吸收的日本先进坡面防护技术——金属框架整体防护技术。
With the consideration of surface tension the boundary integral method and numerical solution method for simulation of a cavitation bubble collapsing near a rigid wall are derived.
导出了考虑表面张力影响下模拟固壁附近溃灭空化气泡特性的边界积分方法及数值求解方法。
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。
That the modified surface current will be given using the method of moments to solve either the electric or magnetic field surface integral equation at the resonant frequencies.
众所周知，在内谐振频率点上，用矩量法求解电场或磁场表面积分方程将得到不正确的表面电流。
In this paper, a new proving of the mean value theorem of integral on surface is given, with some application in related cases presented.
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。
Then with the upper-bound theorem and the surface integral an analytical solution of the drawing stress was first obtained.
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。
Drag of the train head is obtained by the method of surface integral and drag coefficient can be computed at the same time.
通过表面积分的方法得到各种列车车头的阻力，进而计算得到了车头模型的阻力系数。
This article popularizes these methods in the calculation of curvilinear integral and surface integral and gives proof of them as well.
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.
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。
应用推荐