释义 |
- 1
OK, and that surface integral, well, it's not for the same vector field. - 2
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。 - 3
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。
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