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And all this is, is saying that when you take a mixed second derivative, it doesn't matter in which order you take the two derivatives.
麦克斯韦关系的本质是,当你考虑混合的二阶导数时，求导的顺序不影响最后的结果,现在，我们利用这些关系。
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And he knew that about himself and I think that's why maybe he turned out okay at the end.
他了解自己，我想或许是因为这个原因，他最后有了一个好结果。
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Okay. Now ultimately what happens with this is that we begin to take this stream and organize it into different patterns.
好了,这最后的结果,是我们开始把一段无序的节拍流,组合成了不同的模式
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If I go on doing this exercise again, and again, and again what am I going to end up with?
如果我不断重复这个过程呢,最后结果会是怎么样的
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So thankfully, modern operating systems allow you to put parts of files here, parts of your file here, parts of your file here, but the end result is that your files get fragmented.
因此，谢天谢地，现代操作系统允许你,把这里的文件进行分块，在这里存一部分，在那儿存一部分，但最后的结果是你的文件变成了分片的。
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So as a result, they said there were droughts in these areas throughout that period and that caused tremendous unhappiness and discontent.
最后结果就是,他们说那个时期,在那个区域发生了干旱,从而致使,民生凋敝,民怨沸腾
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Because we do try to give as much partial credit as possible in these exams, since there are a lot of places where small mistakes can result in the wrong answer.
因为我们会尽量把能给你的步骤分都给你,在对于这种考试时，因为有很多地方,只要出一点小问题就会导致最后结果出错。
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Now I call that, and it says, 20 tell me how many heads you want, give it a 20, and tell it how many legs 56 you want, give it 56, and it prints out the answers. I know, whoop-dee-doo.
请告诉我你想要几个头，设为，然后告诉它你想要几条腿,设为,最后它会打印结果，哇哦。
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But I showed you in the end how we can use calculus to derive that.
我上节课最后教过你们,如何用微积分来得到那个结果
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One thing that makes it pretty clear is that certainly delta S or the sign of it alone is not dictating the outcome here.
这个例子非常清楚的说明,熵增dS或者它的符号,不能单独决定最后的结果。
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The financial situation is not as bad as it was in the 1930s but it's getting bad and as a result we're starting to see proposals for big change.
现在的金融衍生工具已经不像当年那么拙劣了,但是它却开始走下坡路,所以最后的结果是,我们不得不准备着新的变革。
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And we plug in our values and end up with mv squared mv^2/r-Ze^2/ over r minus Ze squared over And I am going to call this equation two.
我们最后的结果,就是,我把这称为方程式二。
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And we can just extrapolate in a straight line We before saw some examples where I had an algorithm to generate points, and we fit a curve to it, used the curve to predict future points and discovered it was nowhere close.
我们可以干脆用一条直线来描述它,我们之前看到在一些例子中,我用一个算法去生成一些点，然后用一条曲线对它进行拟合，然后用这条曲线来预测未来的点,最后却发现结果完全不对。
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I think it depends on whether the list is odd or even in length. Actually, that's probably not true. With one, it'll probably always get it down there, but if I've made it just equal to two I might have lost.
是奇数还是偶数，事实上,这是不正确的，如果最后剩下一个,那可能得到了结果,如果剩下两个，可能错了,所以，首先我们要格外。
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And you might every once in a while get this, at least as we've done it in this case, this large move out at the end.
一旦你得到了这个结果，至少像是我们在这个例子中得到的结果，最后有一个很大的唯一变化。
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I thought similar to Chris actually and I also thought that if we got two-thirds and everyone was choosing numbers in between 1 and 100 ends up with 33, would be around the number.
实际上我的想法和克里斯的相近,我也在想我们得选平均数的2/3,每个人都在1到100中选择的话,最后结果可能是33,会接近于平均数的2/3
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Well, realize one of the themes in this course and really one of the themes in programming and solving any problem with a machine is going to be really to just take small bites one at a time out of these problems until the end result ultimately is that you've actually bitten off a fairly large fairly interesting problem and in the aggregate, you've actually implemented something pretty sophisticated.
好吧，让我们先想一下这件事带给我们的主题,编程和解决问题的思想,一台机器最开始只会一步一个脚印,沿着要解决的问题向前迈进,直到最终的结果出来,最后你会发现，你已经解决了一个相当大,相当有趣的问题，而这个问题在最初看起来确是相当复杂的。
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I'm gonna run a.out and your teaser for the kinds of programs you can write after years and years and years of practice will give you output like this.
运行a，out，这类麻烦的程序,你多年多年之后也能写,因为最后的结果是这样的。
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And it's just gathering together the multiplications while counting down the exponent. And you can see it when we get down to the end test here, we're going to pop out of there and we're going to return the answer.
这个方法就是通过乘法,来一个一个的减小指数,可以看到,最后面的结果测试，我们会在这里退出,然后返回答案。
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du/dV So now our du/dV, dp/dT at constant T is just T times dp/dT which is just p over T minus p, it's zero.
现在我们的恒定温度下的，等于T乘以dp/dT，在这里,等于p除以T，最后再减去p，结果是0。
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Where's this argument going to go?
最后的结果是什么呢
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What ended up happening is, you know the news, Rupert Murdoch bought The Wall Street Journal last fall and he announced that Wall Street Journal-- WSJ.com--will no longer be free.
最后的结果是,你们知道那条新闻的吧,鲁珀特·默多克去年秋天收购了《华尔街日报》,他宣布《华尔街日报》,WSJ.com,将不再免费
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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。
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And along the way I'm keeping track of how many iterations at the end I'll print how many iterations I took, before I return the final guess.
提到的方法去运行,并且我会跟踪到底,进行了多少次迭代,并在最后返回结果之前，显示进行了多少次迭代。
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And we put all that together and here is what it looks like.
我们把所有统一起来,这就是最后结果的表达形式。
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So in this experiment here, delta p is less than zero. You need to have this whole thing greater than zero. So delta T is less than zero as well. So if you're below the inversion temperature and you do the Joule-Thomson experiment, you're going to end up with something that's colder on this side than that side.
所以在这个实验中，Δp小于零,这全部都大于零,因此ΔT也小于零,所以如果在低于转变,温度的情况下做焦耳-汤姆孙实验,最后的结果是,这边的温度比这边低。
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