line integral

An Improved Proof of a Necessary Condition for the Independence fo the Path of a Line Integral

对曲线积分与路径无关的一个必要条件的改进证法

It tells us, if you compute the line integral along C1, it's just f at this point minus f at this point.

它告诉我们，如果沿C1计算线积分，结果就是f在这点的值减去在那点的值。

Then I can actually& replace the line integral for flux by a double integral over R of some function.

那么我就能名正言顺地，用R上的某个函数的二重积分来替代通量的线积分。

New Meth to Prove Computational Formulas of Line Integral and Surface Integral

曲线积分与曲面积分计算公式的新证明

This paper derives Maxwell's equations in differential form for the existence of magnetic monopoles from Coulomb's law of static interaction between point magnetic charges and Ampere's law for a line integral of around a closed path, The author describes an electromagnetic picture.

本文从真空中磁的库仑定律和电的安培环路定律推导出磁单极存在下麦克斯韦方程组的微分形式，描绘出磁单极存在下的电磁图象。

One of them involves computing a line integral from the origin to a point in the plane by going first along the x axis, then vertically.

一种是从原点开始，沿x轴水平前进，然后沿y轴竖直前进，求出相应的线积分。

Analysis of Microstrip-Waveguide Transition by Line Integral Method in Spectral Domain

微带波导过渡接头的谱域线积分法分析

So that will be the line integral of Pdx plus Qdy.

这就变成了Pdx+Qdy的线积分。

Or, if you really don't like that line integral, you could close the path by adding some other line integral to it, and then compute using Green's theorem.

如果不喜欢计算线积分，可以通过增加一条线积分让曲线封闭起来，然后就可以用格林公式来计算了。

A new proof on independence of path of a line integral

曲线积分与路径无关的另一证法

If the field changes slowly, we can replace the time integral by a line integral over the unperturbed orbit.

如果场缓慢改变，我们能够用未扰动轨道的线积分来代替时间积分。

Just as we do work, when we compute this line integral, usually we don't do it geometrically like this.

就像做功一样，当计算这线积分时，通常不这样用几何方法来做。

Well, remember we said yesterday that the line integral of F dr, Tds maybe I should say F dot T ds now, because the vector field is tangent to the circle.

记住昨天提到过的，Fdr的线积分，或者F•，因为这些向量都是圆的切线。

The results are of use value for simplifying the computation of line integral and surface integral.

这一结果,对于简化线积分、面积分的计算具有使用价值.

Several Principles of Symmetry for the Line Integral of Vector Fields on the Plane

平面上第二类曲线积分的对称原理

Necessary and Sufficient Conditions for Path Independence of a Line Integral in a Complex Connected Region

复连通区域曲线积分与路径无关的充要条件

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。

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。