We want to integrate. So let's take the integral of both sides, going from the initial point to the final point.

分别从初态,到末态做积分，消去微分。

麻省理工公开课 - 热力学与动力学课程节选

And that brings me to my final point about our Hobbesian civilization that conceals from us a very uncomfortable truth.

接下来我要讲的,是霍布斯现代文明观的最后一个观点,它将把一个残酷的现实呈现在我们面前。

耶鲁公开课 - 政治哲学导论课程节选

So there's going to be a line that's going to connect the initial point to the final point, and that line mathematically is not going to be the same as this one here.

连接绝热过程,初末态的曲线的方程，和等温线的方程,也不会相同。

麻省理工公开课 - 热力学与动力学课程节选

And the final point I want to make today, and this is very, very important, so make sure that you do understand this.

而今天我要强调的最后一点，也是非常，非常重要的一点，因此请务必真正理解它。

麻省理工公开课 - 化学原理课程节选

The final point that I want to make with respect to security selection actually is a little bit different with the degree of opportunity.

我想说的最后一点是,就证券选择而言,运气也会带来一些差别

耶鲁公开课 - 金融市场课程节选

The point here--final point and then I'll let you go.

这里的要点是,最后一个要点,说完就下课

耶鲁公开课 - 聆听音乐课程节选

Final point then is...and we're not going to talk about salvation right now...but we're going to talk about the fact that the only supreme law is the will of God, because God is a creator God rather than a created God. He's imposed order, an order upon the cosmos.

最后一点，我们并不准备马上讲救赎,我们准备讲的事实是唯一的,至高无上的法律就是上帝的意愿，因为上帝是一个创造者,而不是被造出来的上帝，他对宇宙发号施令。

耶鲁公开课 - 旧约导论课程节选

The final document I want to use to make the point here comes from precisely the poems of Solon.

我陈述此观点所用的最后一份文献资料,来自梭仑的诗歌

耶鲁公开课 - 古希腊历史简介课程节选

And the third thing I need to decide is how do I combine? You know, point out to you in the binary search case, combination was trivial. The answer to the final search was just the answer all the way up.

第三个问题是我需要决定如何进行合并？,就你们所知的，在二分查找中所打印出来的,合并的过程是非常简单的,最后查询的结果,就是一路上来所以的结果。

麻省理工公开课 - 计算机科学及编程导论课程节选

I have to warn you this third and final movie is an example of why this research is not currently done, but it illustrates an important scientific point.

我必须警告你们第三,和最后的影片是一个例子,关于为什么这个研究现在没有做，但它描述了重要的科学观点。

耶鲁公开课 - 心理学导论课程节选

And so, the philosopher, who has sort of trained himself to separate his mind from his body, to disregard his bodily cravings and desires-- the philosopher will welcome death because at that point he'll truly, finally, make the final break from the body.

所以,那些,已经为灵魂脱离肉体,以及忽视自己的肉体欲望,做好准备的哲学家,将会欢迎死亡的到来,那时他会真正地,最终地,从自己的肉体中解脱出来

耶鲁公开课 - 死亡课程节选

If it was non-reversible, I would be allowed to put an initial point and a final point, but I wouldn't be allowed to put a path between them like this, connecting them together.

如果是不可逆过程，我可以画出过程的初态点,和末态点，但是我不能再像这样,画出连接这两个点的，路径曲线来。

麻省理工公开课 - 热力学与动力学课程节选

The sum of path number 2 and path number 3 get me to the same place, so the energy change by going through this time path, this intermediate point here back all the way to final state should be the same the red path.

而经过路径2和3可以3,到达同样的末态，因此经过路径,2和3带来的能量的变化，与路径1带来的,能量变化相同。

麻省理工公开课 - 热力学与动力学课程节选