OK, and now we return to this differential.

好，让我们回到这个微分式。

麻省理工公开课 - 热力学与动力学课程节选

We can measure the heat capacity at constant volume, and now we have another term, and if we can figure out how to measure it, we'll have a complete form for this differential du which will enable us to calculate du for any process.

我们能够测量恒定体积下的热容，这里我们有另一项，如果能够知道怎么测量它，问我们就有了这个完整的微分式,就能够对任何过程计算。

麻省理工公开课 - 热力学与动力学课程节选

So, let's say we start off at the distance being ten angstroms. We can plug that into this differential equation that we'll have and solve it and what we find out is that r actually goes to zero at a time that's equal to 10 to the negative 10 seconds.

也就大约是这么多,所以我们取初始值10埃,我们把它代入到,这个微分方程解它,可以发现，r在10的,负10次方秒内就衰减到零了。

麻省理工公开课 - 化学原理课程节选

Here you've got a red light which doesn't seem to enter into this sense of the arbitrary and differential.

这里，红灯看起来并没有,任意性和差异性。

耶鲁公开课 - 文学理论导论课程节选

This is a calculus-based class and I expect everyone to know at least the rudiments of differential calculus.

这门课需要微积分的数学基础,我觉得每个人至少应该知道,一些微积分的基础知识

耶鲁公开课 - 基础物理课程节选

MI stands for heart attack, myocardial infarction, and in this case you see an even bigger differential of people with a metabolic syndrome having even more elevated risk then they did for stroke.

I表示心脏病发作,心肌梗塞,在此可以看到患有代谢综合征的患者,比非患者心脏病发病风险更高

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

So, all you will have the opportunity to solve differential equations in your math courses here. We won't do it in this chemistry course. In later chemistry courses, you'll also get to solve differential equations.

你们在数学课中有机会,遇到解微分方程,我们在这化学课里就不解了,在今后的化学课程里，你们也会遇到解微分方程的时候。

麻省理工公开课 - 化学原理课程节选

So the delta v here is an exact differential, but this dw is not.

你是如何,到达这个状态的。

麻省理工公开课 - 热力学与动力学课程节选

And this little slash here means an in inexact differential.

请注意这里的小横杠,说明这不是一个准确的微分。

麻省理工公开课 - 热力学与动力学课程节选

When you say that, it implies that the differential is given by this pair of partial derivatives.

这就意味着，内能的微分,等于偏u偏T，保持体积不变。

麻省理工公开课 - 热力学与动力学课程节选

So that what's new in Saussure's thinking about the relationship between signified and signifier is that the sign tied up in this relationship is both arbitrary and differential.

这就是索绪尔所贡献的了,能指和所指的关系,也就是符号的组成方式,是任意的，有差别的。

耶鲁公开课 - 文学理论导论课程节选

We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.

我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。

麻省理工公开课 - 热力学与动力学课程节选

You won't have to solve it in this class, you can wait till you get to 18.03 to start solving these types of differential equations, and hopefully, you'll all want the pleasure of actually solving the Schrodinger equation at some point. So, just keep taking chemistry, 18 03 you'll already have had 18.03 by that point and you'll have the opportunity to do that.

你们不用在课堂上就解它，你们可以等到得到18，03之后,再开始解这些类型的微分方程，希望你们都想得到,实际解薛定谔方程的乐趣,所以，保持来上化学课，你们在那个点将会得到,你们有机会做到的。

麻省理工公开课 - 化学原理课程节选

But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.

但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。

麻省理工公开课 - 化学原理课程节选