So, these are special cases of what's called the fundamental theorem of calculus for line integrals.

这些都是反映了,线积分的微积分基本定理的特例。

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So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.

微积分基本定理，不是曲线积分的，告诉我们，如果对函数的导数积分，就会得回原函数。

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Moreover, we also get a fixed point theorem of uniform partial extension mapping and a fixed point theorem of quasi-extension mapping.

另外，我们还得一个一致局部扩张映射不动点定理与一个准扩张映射不动点定理。

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First of all, it's clear from the Pythagoras' theorem that a is the square root of ^2 + ^2.

首先,根据毕达哥拉斯定理,勾股定理在西方被称为"毕达哥拉斯定理"

耶鲁公开课 - 基础物理课程节选

So there are examples in American History of elections that seem to in which the Median Voter Theorem seems to do well.

因此从美国历史上的选举案例里看,中位数选民定理非常奏效

耶鲁公开课 - 博弈论课程节选

And it turns out there's a variety of proofs of the Pythagorean Theorem.

其实有很多种证明勾股定理的方法

耶鲁公开课 - 死亡课程节选

The idea behind both proofs of the four colour theorem is to suppose that the theorem is violated to assume, in other words, that there is some sort of map that requires five colours to fill in.

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With research continuing into this strand of ancient history, it remains to be seen whether Pythagoras's theorem will come to bear the name of an old Babylonian scribe instead.

CNN: Pythagoras, a math genius? Not by Babylonian standards

The significance to me of the Coase Theorem is that it undermines the Pigovian system.

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