I signed those fiches, those formulas and if I hadn't been there to save the hundreds then they all would've died."
我签了那些文件,那些表格,要不是我救那几百人,他们就都死了"
As we see a little bit later, I could talk about the carbon-hydrogen bond in methane where there is a plurality of bonds. In this case, there is only the one bond but I just want to get the formulas.
因为我们后来看到一点点,我能讨论甲烷中的碳氢共价键,那有许多共价键,这种情况下,这只有一条共价键,但我想得到氟。
So we came up with two formulas, which are similar to the two that I'm showing here.
所以我们得到了两个公式,它们和我展示这两个,很类似。
These are all formulas, I just plugged it into formulas that we did in the second lecture.
这些就是计算要用到的所有的变量,把它们代入第二节课,讲过的公式中去。
So, we are now going to do one standard problem where we will convince ourselves we can apply this formulas and predict the future given the present.
我们接下来将去研究一个标准问题,通过这个问题,我们能让自己相信,我们能利用这些式子,根据现状,预测未来
And so we might need to work out various, more complicated, formulas here, where we multiply the pain times its duration and take into account its intensity, get the sheer quantity of pain that way.
我们需要编制出各种,更复杂的公式,以便增加痛苦的倍数,延续时间,还要考虑痛苦的强度,获得痛苦的纯量。
So how would we go about solving this problem if I told you not only was there a maximum weight, but there was a maximum volume. Well, we want to go back and attack it exactly the way we attacked it the first time, which was write some mathematical formulas.
有些时候两个都重要,所以如果我告诉你这里不仅有,最大重量还有最大容量,我们应该怎么解决这个问题呢?,好了,我们想回过来然后,和第一次一样看看这个问题。
We have formulas for these present values and these formulas are well known.
我们有几个公式,来计算现值,这些公式相当有名
So what we need to do here is use the Rydberg formula, and actually you'll be given the Rydberg formulas in both forms, both or absorption and emission on the exams.
我们需要用到Rydberg公式,事实上,在考试时,我们会给你们Rydberg公式的两种形式。
In the early days when there are four or five formulas, you could memorize all of them and you can try each one of them until something works, but after a couple of weeks you will have a hundred formulas and you cannot memorize all of them.
刚开始我们只会涉及到四,五个公式,你可以全部记下来,你可以一个一个试,直到解出答案,但过了几个星期,你就已经学了一百多个公式了,你没法全部记下来
So, essentially when we're talking about these equations up here, all we're doing is talking about the regular Rydberg formulas, but instead we could go back and re-derive the equation for any one electron atom, which would just mean that we put that z squared term in the front.
所以本质上,当我们讨论,这些问题时,我们说的是常规的,Rydberg公式,但对任何其他单电子原子,我们不用,从头再推到,而是仅仅把,z平方项放在前面。
That's one of the most basic formulas in finance.
它是金融领域中最基本的公式
The way you would go about it, if you're a portfolio manager, is you have to come up with estimates of the inputs to these formulas-- that means the expected returns, the standard deviations, and the covariances.
你所要做的,如果你是一个资产经理,你要做的事情就是,对公式里面的一些参数进行估计-,那些参数包括预期收益,标准差,和协方差。
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