- 1. So, in fact, it's a vector field.
- 事实上，是一个向量场。
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- 2. We have this vector field.
- 这是向量场。
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- 3. That was a vector field in the plane.
- 它是一个在平面上的向量场。
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- 4. That is my curve and my vector field.
- 那就是曲线和向量场。
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- 5. It is proportional to this vector field.
- 它与向量场成比例。
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- 6. We dot our favorite vector field with it.
- 用我们喜欢的向量场来点乘它。
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- 7. And my vector field.
- 向量场。
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- 8. So, this vector field is not conservative.
- 所以，这个向量场不是保守场。
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- 9. That is called the curl of a vector field.
- 这个量叫向量场的旋度。
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- 10. Well, our vector field, is actually vertical.
- 向量场是竖直的。
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- 11. At the origin, the vector field is not defined.
- 在原点，向量场是没有意义的。
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- 12. Let's say I want to do it for this vector field.
- 比如说，我想对这个向量场来求解。
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- 13. F I have my surface and I have my vector field f.
- 有一个曲面，还有一个向量场。
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- 14. OK, so you take the divergence of a vector field.
- 取一个向量场的散度。
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- 15. One is the vector field whose flux you are taking.
- 一个是要取通量的向量场。
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- 16. I want to find the potential for this vector field.
- 我想找出这个向量场的势函数。
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- 17. Let's say that our vector field has two components.
- 假设我们的向量场有两个分量。
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- 18. The problem is not every vector field is a gradient.
- 问题是，不是所有向量场都是梯度。
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- 19. 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。
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- 20. We had a curve in the plane and we had a vector field.
- 平面上有一曲线，且存在着向量场。
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- 21. But now, let's say that I have a general vector field.
- 但是现在，假设有一个一般向量场。
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- 22. 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。
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- 23. 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。
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- 24. OK, so my vector field does something like this everywhere.
- 这个向量场处处都是这样。
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- 25. Let's say that we had the same c, but now the vector field.
- 假设c还是一样的，但现在的向量场变为。
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- 26. That actually is what we will call later a vector field.
- 这就是后面我们要讲的向量空间。
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- 27. 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。
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- 28. But that assumes that your vector field is well-defined there.
- 那是假定了向量场是有定义的。
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- 29. We need, actually, a vector field that is well-defined everywhere.
- 实际上我们需要，一个处处有定义的向量场。
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- 30. 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。
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