我们称这种变数为密度微分。
这种毡制品只是为了消除与塑料产生太多的摩擦力，或者让它与外壳稍微分开。
This felt thing there is just to avoid too much friction from building up with the plastic or to keep it slightly separated from the case.
这种毡制品只是为了消除与塑料产生太多的摩擦力，或者让它与外壳稍微分开。
This felt thing there is just to avoid too much friction from building up with the plastic or to keep it slightly separated from the case.
所以你要做的第一件事是你写下，你的微分方程。
So the first thing you do is your write down your differential equations.
因此可以马上写下，这个微分方程的，解法。
So you can write down immediately the solution to this differential equation.
你们有些人也许已经，解出了微分方程。
这是整个机理的完整的微分方程，不是它的一部分。
This is the full differential equation for the full mechanism. Not just one part of it.
只是在用微分的语言表达，来看先前提到的例子。
Just in the language of differentials. The example that I promised.
这个微分方程的，解法是什么呢？
得到一个微分方程。
要完全了解本课程，应必备微积分和微分方程的知识。
Calculus and Differential Equations are highly recommended for full understanding of the course.
几个微分方程。
这是一个我们先前不了解的精密复杂的微分信号系统。
This is a sophisticated differential signaling system that we haven't previously known about.
我们要解决，两个成对的微分方程，这是无法解决的任务。
And so now we have to solve two coupled differential equations, which is a hopeless task.
请注意这里的小横杠，说明这不是一个准确的微分。
And this little slash here means an in inexact differential.
顺便说一下，也可以从微分的角度来考虑。
By the way, we can also think of it in terms of differentials.
好的我们可以看这儿,看这个微分方程，这里没有做近似。
Well we can go look up here, looking at the differential, there are no approximations here.
这是个微分方程。
我们可以用微分，就像这样，也可以用链式法则。
Well, we could use differentials, like we did here, but we can also keep using the chain rule.
我们不再讨论微分方程序。
我们已经讲了微分。
这是一个非常，简单的微分方程，两边积分。
Namely, this is still a pretty straightforward differential equation. So let's just integrate both sides.
应该会有疑问的，而且还是不太相信微分，那么我的证明过程中，多次用到的微分符号，就有问题了。
Let's say that you are a true skeptic and you don't believe in differentials yet then it is maybe not very good that I actually used more of these differential notations in deriving the answer.
这就是“什么是微分？这个式子是什么？”，最普遍的回答。
I would say that is the most general answer to what is this formula, what are these differentials.
这个就是微分。
这无关紧要，我们用微分是怎样做的？
It doesn't really matter. So, how do we do things using differentials?
我们来看g的微分。
我们已经写出了一个微分方程。
这个是符号化的向量算子，其中它的分量是偏微分算子。
That was this symbolic vector operator in which the components are the partial derivative operators.
为什么我们偏爱偏微分呢？
应用推荐