A lot of damage was caused by this crisis. It is going to take some time for us to grow out of this.
VOA: standard.2009.11.01
By the time you get to the end of the term, you're going to be dealing with some fairly complex things, so one of the things you're going to see is, we're going to make heavy use of libraries, or code written by others.
当你临近期末的时候,你们将要解决一些,相当复杂的难题,因此你们将会看到的其中一点是,我们要充分利用图书馆,或者别人编写的代码。
OK, in a few minutes we're going to start talking then about what is computation, how are we going to start building those tools, but that's what you should take away, that's what you're going to gain out of this course by the time you're done.
好啦,我们会花一点儿时间,谈谈什么是计算,我们如何去建造这些工具,但是这些是你应该,在离开这个课堂时,应该学会的事儿。
The other tip I'm going to give you is any time you see a chain molecule, by chain I just mean many different atoms written out in a row.
我要告诉大家的另外一个小窍门是,每当你看到一个链状分子,链状的意思是说很多,不同的原子写成一行的形式。
So, I'm not going to waste your time by asking what happens if you put it in.
我不会问你们把式子带进去以后怎么算,这完全是浪费时间
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。
So rather than go through this again a whole third time, I've gone through it once in quantities and once in prices, I'm going to get you guys to do it this time by having you do it on a homework assignment.
与其从头到尾再做第三遍,我已经从产量和价格角度从头到尾做过了,我将让你们自己,在家庭作业中完成这个工作
So this is a question that I want to continue today, to consider what the trial of Socrates means and I want to begin by going back to a problem or a paradox that I ended the class with last time.
这就是我今天要继续的问题,考虑苏格拉底受审的意义,我想要先回到一个问题,一个悖论,也是我们上堂课所遗留的。
This is going to end up at a different temperature by the way. You saw this last time in a slightly different way. Last time what you saw is we compared isothermal and adiabatic paths that ended up at the same final pressure, and what you saw is that therefore they ended up in different final volumes.
末态温度是不一样的,上次你们看到的,和这个有一点不一样,上次我们比较的是末态压强,相等的等温过程和绝热过程,因此它们的末态,体积是不一样的。
You're all going to be great chefs by the time you're done here. All right?
你们完成这门课后,都会成为大厨对不对?
So, you can understand they really felt quite confident at this time that we could explain everything that was going on and in fact, a really telling quote from the time was said by a professor at the University of Chicago, and what he said is, "Our future discoveries must be looked for in the sixth decimal place."
所以你可以理解,为什么当时的人那么,自信的说我们可以解释,这世界上发生的一起事情,事实上,当时有个著名的名言,是芝加哥大学的一个教授说的,他说“我们今后的科学发现,就在于弄清楚小数点第六位后的数,“
I think you can tell by analogy with what I did in one dimension that the position of that object at any time t is going to be the initial position plus velocity times t plus one half a t square.
你们可以类比一下我在一维情况下的结论,这个物体在任意时刻 t 的位移,等于初始位移,加上 v ? t + 1/2 ? a ? t^2
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