In statistical physics lectures, the calculation of the configuration partition function of molecule is simplified from double vectors integral to single vector integral.
统计物理教材中分子构型配分函数的计算，一般是将双矢量积分化简为单矢量积分。
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。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
So, in both cases, we need the vector field to be defined not only, I mean, the left hand side makes sense if a vector field is just defined on the curve because it's just a line integral on c.
了解这两种表述后，我们不仅需要向量场，就是左边这里，这是曲线c上的线积分，向量场在曲线上有定义。
So, to say that a vector field with conservative means 0 that the line integral is zero along any closed curve.
一个保守的向量场就是说,沿任意闭曲线的线积分的结果是。
So, one of them says the line integral for the work done by a vector field along a closed curve counterclockwise is equal to the double integral of a curl of a field over the enclosed region.
其中一种说明了，在向量场上，沿逆时针方向，向量做的功等于，平面区域上旋度F的二重积分。
So, we need to set up the flux integral for a vector field dot ndS.
需要建立向量场点乘nds的通量积分。
I'm going to prove that the flux of a vector field that has only a z component is actually equal to the triple integral of, RzdV well, the divergence of this is just R sub z dV.
我将要证明，一个只有z分量的向量场的通量,等于一个三重积分，其中被积表达式为。
S if we have a closed surface with a normal vector pointing outwards, and we want to find a flux integral for it, well, we can replace that with a triple integral.
的法向量似乎是指向外部。，And, the,normal, vector, to,s, seems, to, be, pointing, out wards, everywhere。，如果我们有一个法向量指向外部的封闭曲面，并且我们要求出它的一个通量积分，那么我们可以用一个三重积分来代替这个通量积分。
So, that means that the double integral for flux through the top of R vector field dot ndS becomes double integral of the top of R dxdy.
这就是说通量的二重积分,顶部R•ndS的二重积分,变成了Rdxdy的二重积分。
A part of results on magnetic vector potential of circular loop are expanded, so the integral function is transformed to integrable series.
采用将圆电流磁矢势表达式中一部分展成级数，使被积函数变成可积分的函数。
It is suggested that transformation relation between spatial local coordinate system and integral coordinate system be established by vector method, which simplifies coordinate calculation of to.
提出了运用向量法建立空间局部坐标系与整体坐标系的转换关系，从而使趾板坐标计算简捷方便，且易于设计修改。
This paper discusses submanifolds with parallel mean curvature vector in local symmetric Spaces and obtains integral invariants about the square of modulus-length.
讨论局部对称空间中具有平行平均曲率向量的子流形，得到其关于第二基本形式模长平方的积分不等式的相关定理。
The vector surface integral equation can't be applied to numerical computation directly because its integrands possess the high order singularity.
矢量的面积分方程因其被积函数具有高阶奇异性，不能直接应用于数值计算。
A new control algorithm is proposed in this paper. That is the unit vector with a integral corrective term adaption law.
本文提出了一种自适应控制算法：单位向量加积分校正自适应算法。
The near orthogonal hierarchical vector basis functions are used for solving three-dimensional time-domain electromagnetic integral equations (TDIE) of the metallic object.
本文将准正交高阶叠层矢量基函数用于时域电磁场积分方程(TDIE)，求解了三维金属目标的时域电磁散射问题。
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。
To do that, the integral definition of vector magnetic potential and the Lorentz gauge is used to expand the integral equation of the PEEC model.
为此它以矢量磁位的积分表达式和洛仑兹规范代替了矢量磁位和标量电位的积分表达式，对积分方程进行展开。
Some knowledge of vector calculus assumed. Maxwell's equations, in both differential and integral form.
像是向量微积分、微分和积分形式的麦斯威尔方程序。
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。
A strategy of speed control for vector-controlled asynchronous motor drive system using sliding mode variable structure control with an integral action was proposed.
针对滑模变结构控制的抖振问题，提出一种用于异步电动机矢量控制系统的积分滑模变结构速度控制方法。
Compensation feedback flux was automatically adjusted through a proportional-integral (PI) regulator by checking the perpendicular degree of flux vector with back EMF vector.
通过检测反电势和磁链的正交程度来自动调节磁链补偿程度，以获得磁链的精确观测值。
In source-free plasma anisotropic medium, the electromagnetic fields can be expressed as integral of the first and the second spherical vector wave functions.
根据不同类型的矢量球波函数，建立无源各向同性球层内以及自由空间内的电磁场在球坐标系下的级数表达式。
In source-free plasma anisotropic medium, the electromagnetic fields can be expressed as integral of the first and the second spherical vector wave functions.
根据不同类型的矢量球波函数，建立无源各向同性球层内以及自由空间内的电磁场在球坐标系下的级数表达式。
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