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.
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.
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.
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。
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。
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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