Now, we are very gentle in this course with respect to knowing integrals, but this is one you have to know.

这门课对积分,的要求并不高，但这个积分你们必须会算。

麻省理工公开课 - 热力学与动力学课程节选

There's still a lot more of the text and so that first fragment a part, but I immediately begin to form an opinion about this part with respect to an imagined or supposed whole.

文本中的很多还没有读，但是那第一个片段成为了一个局部，但是我立即对这个局部有了自己的想法,并且开始设想全文。

耶鲁公开课 - 文学理论导论课程节选

We can start taking derivatives of this with respect to time.

我们首先来对时间求微分

耶鲁公开课 - 基础物理课程节选

In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.

换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。

麻省理工公开课 - 热力学与动力学课程节选

I'm going to treat this chapter as a sort of microcosm of the book, with respect to its craft. Let's look at how this opens: "The next afternoon when he got his car back, he drove it out into the country to see how well it worked on the open road.

我认为这一章是整本书的缩影，关于这个的写法，让我们一起看一下她是如何开头的：,第二天下午，当他拿回自己的车时，他把它开出去,开到农村里，想看看开着它在平坦的公路上时，它的性能如何。

耶鲁公开课 - 1945年后的美国小说课程节选

We'll be doing this in one week, and the disjunction between the two works, this disjunction at least with respect to their treatment of the Fall, should dramatize the nature, or just the enormity, of a lot of the conceptual problems and conflicts that Milton is tackling here.

我们在一周内都会来做这个工作，将这两部著作分离开来，这种分离至少要尊重他们对秋天不同的理解，应该将自然戏剧化，还是只是极恶,弥尔顿在这里应对的很多观念上的问题和冲突。

耶鲁公开课 - 弥尔顿课程节选

I differentiate a second time and check the sign, so the second order condition, I differentiate this expression again with respect to q1.

我们对它进行二次求导然后看符号,这个式子的二阶导数,就是一阶导数再对q1进行求导

耶鲁公开课 - 博弈论课程节选

I think it's clear, the position of the object with respect to the ground, this vector is the same as the position of the object with respect to the plane, plus the position of the plane with respect to the ground.

我觉得很明显,物体相对于地面的位置,这个矢量等于,物体相对于平面的位置矢量,加上物体相对于地面的位置矢量

耶鲁公开课 - 基础物理课程节选

We're going to differentiate this with respect to q1 and then what?

对q1求导之后还要做什么

耶鲁公开课 - 博弈论课程节选

So I'm going to differentiate this object again with respect to S1,.

我们再次对S1求导

耶鲁公开课 - 博弈论课程节选

And the point is that the second derivative of A, with respect to V and T in this order is the same as the second derivative of a with respect to T and V in this order.

问题的关键在于A的二阶导数，对V和T以这样一个顺序求导,和对T和V以这样一个顺序,求导是一样的。

麻省理工公开课 - 热力学与动力学课程节选

du/dT constant pressure is the direct derivative with respect to temperature here, which is sitting by itself under constant volume keeping this constant but there is temperature sitting right here too.

偏U偏T，p恒定是对,温度的直接微分，而它本身对体积不变,保持它不变，但是这里也有一个温度,这就是偏U偏V，T恒定。

麻省理工公开课 - 热力学与动力学课程节选

What I did was I differentiated this fairly simple function with respect to q1 and since I want to find a maximum, what I'm going to do is I'm going to set this thing equal to 0.

只不过是对q1求导了,既然我们要求出最大值,只需要令导数等于0就可以了

耶鲁公开课 - 博弈论课程节选