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.
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.
当你试图接住一个飞行中的球时，是否会通过解微分方程来确定自己的位置？
Do you position yourself to catch a ball by solving differential equations in your head, on the fly?
在方程课上，我听了一系列未公开的演讲，强调的是微分方程的解的存在证明及其唯一性。
For the equations course, I was given a set of unpublished lectures that emphasized existence proofs and uniqueness of solutions to differential equations.
相反，为了证明“红色效应”，我应该使用一张一个老男人用红笔求解微分方程系统的图像。
Instead, to demonstrate the "red effect" I should have used an image of an elderly man solving a system of differential equations using a red pen.
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。
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.
再说明一下，这是关于这两个向量场，多少有点奇怪的偏微分方程。
And just to tell you again that is a strange partial differential equation relating these two vector fields.
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.
总的来讲，所有你想解决的问题，都可以用偏微分方程来做。
Basically, to every problem you might want to consider there is a partial differential equation to solve.
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.
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.
它们唯一共同之处就是,它们都被叫作一阶微分算子。
The only thing they have in common is that both are what's called a first order differential operator.
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.
行程化学计量给你一个关系，你可以用来，代入进你的微分方程。
This is what you started with, a, a So stroke stoichiometry give you a relationship, which you can use to plug into your differential equation here.
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.
微分区和虚拟化。
对你们来说这可能很让人头疼，就像你们在5。60里体验过的那样，这有很多偏微分和变量。
This should be particularly bothersome to you because, as you've already experienced in 5.60, There are a lot of partial derivatives.
微分区是一个强大的特性，它允许您最大效率地利用处理器资源。
Micro-partitioning is a powerful feature that allows you to leverage your processor resources with maximum efficiency.
微分区是一个强大的特性，它允许您最大效率地利用处理器资源。
Micro-partitioning is a powerful feature that allows you to leverage your processor resources with maximum efficiency.
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