我们还学过微分的链式法则，也就是用其他量来代替这些偏导数。

So, we've learned about differentials and chain rules, which are a way of repackaging these partial derivatives.

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现在可以看到，全微分里面的这些偏导数系数，都可以用一个变量表示出来。

Now you see how the total differential accounts for, somehow, all the partial derivatives that come as coefficients of the individual variables in these expressions.

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采用了压缩性的坐标变换后，推导得到了五个一阶导数的微分方程组。

Using a compressibility coordinate transformation, a set of the first derivative differential equations has been derived.

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So here I've written for the hydrogen atom that deceptively simple form of the Schrodinger equation, where we don't actually write out the Hamiltonian operator, but you remember that's a series of second derivatives, so we have a differential equation that were actually dealing with.

这里我写出了,氢原子薛定谔方程的,最简单形式，这里我们实际上,没有写出哈密顿算符,但是请记住那你有，一系列的二次导数,所有我们实际上会处理一个微分方程。

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So, using those, now, what happens if we take the second derivative of A, the mixed derivative, partial with respect to T and the partial with respect to V.

如果我取A的二阶导数,混合导数，对T偏微分,再对V偏微分。

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In other words, your job is to guess a function whose second derivative is a, and this is called integration, which is the opposite of differentiation, and integration is just guessing.

换言之,你的任务是要猜出一个二阶导数为a的函数,这就是积分,和微分恰恰相反,积分就是猜

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