Magnetic gradient tensor is that the three components of the magnetic field vector space rate of change, is able to do well for the dipole localization and tracking.
磁力梯度张量表示的是磁场矢量三个分量的空间变化率，能够很好地用于偶极子场源的定位跟踪。
The analytical expressions for the dynamic stresses and perturbation of magnetic field vector are obtained by means of a finite integral transform and Laplace transform.
给出一种解析方法求解在两种热载荷冲击作用下，正交各向异性圆柱体的动应力和磁场矢量扰动的集中效应。
The integral relationships of time-harmonic electromagnetic field vector are given, the effective sours of radiative fields is Studied, then some examples are calculated.
给出时谐电磁场矢量的积分关系式，探讨了辐射场的有效源，并应用于几个实例的计算。
Magnetic field vector is a function of the position where the satellite stays. Thus autonomous navigation for small satellite can be achieved by measuring the magnetic field vector.
地磁场矢量是卫星所在位置的函数，通过对地磁场的测量，即可实现对近地小卫星的自主导航。
We dot our favorite vector field with it.
用我们喜欢的向量场来点乘它。
Once you have such a formula, you do the dot product with this vector field, which is not the same as that one.
一旦你得到一个这样的计算式，你对向量场做点积，这和前面这个不一样。
We have a vector field that gives us a vector at every point.
有一个向量场来描述每一个点上的向量。
Well, I want to figure out how much my vector field is going across that surface.
下面我们要搞清楚，这个向量场是如何穿过曲面的。
So, the divergence theorem gives us a way to compute the flux of a vector field for a closed surface.
散度定理为我们提供了一种，计算向量场通过闭曲面的通量的方法。
The curl of a vector field in space is actually a vector field, not a scalar function. I have delayed the inevitable.
空间中的向量场的旋度，是一个向量场，而不是一个标量函数，我必须告诉你们。
At the origin, the vector field is not defined.
在原点，向量场是没有意义的。
Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
In fact, our vector field and our normal vector are parallel to each other.
事实上，给定的向量场与法向量是相互平行的。
My vector field is really sticking out everywhere away from the origin.
即给定的向量场是以原点为心向外延伸的。
The problem comes from a vector field satisfying this criterion in a region but it has a hole in it.
如果一个向量场，在一个有洞的区域上，满足这个条件，就会出问题。
I have a curve in the plane and I have a vector field.
这有一条平面曲线和一个向量场。
It's a vector field that just rotates around the origin counterclockwise.
这是一个绕原点逆时针旋转的向量场。
What we will do is just, at every point along the curve, the dot product between the vector field and the normal vector.
我们要做的是，沿着曲线的每一点上，取向量场和法向量的点积。
It measures how much a vector field goes across the curve.
它度量有多少向量场穿过了曲线。
But that assumes that your vector field is well-defined there.
那是假定了向量场是有定义的。
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
如果说函数的梯度是向量，那么向量场的散度就是函数。
Well, actually here it is not very hard to find a function whose gradient is this vector field.
实际上，找出一个函数，其梯度是这个向量场并不难。
If you take a vector field that is a constant vector field where everything just translates then there is no divergence involved because the derivatives will be zero.
如果取的向量场是处处恒定的，所有点都是平移关系，所以没有散度，因为导数为零。
Now, an important difference between curl here and curl in the plane is that now the curl of a vector field is again a vector field.
和平面上的旋度的一个重要的不同点是，这里向量场的旋度，仍然是一个向量场。
One is the vector field whose flux you are taking.
一个是要取通量的向量场。
You have seen that in the plane it is already pretty hard to draw a vector field.
正如大家所知，在平面中画出向量场已经很困难了。
It is a vector field in some of the flux things and so on.
也可以是一个向量场的通量，等等。
Let's say that I have a plane curve and a vector field in the plane.
有一条平面曲线和这个平面上的向量场。
Well, it looks like positive should win because here the vector field is much larger than over there.
看上去正的会多一点,因为这里的向量场要大一些。
Well, it looks like positive should win because here the vector field is much larger than over there.
看上去正的会多一点,因为这里的向量场要大一些。
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