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Coll says NATO plans to create an environment of security in Kandahar that would allow Afghans to create fresh political equations.
VOA: standard.2010.05.28
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We've used the fundamental equations that are hiding down here, out of sight but never out of mind.
我们利用了,写在这里的基本方程，虽然没有注意它但却时时刻刻记者它。
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But we can use equations that describe waves to describe matter, and that's what we're going to be doing today.
但我们可以用描述波的方程,来描述物质，这就是我们今天要做的。
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Now, it's also very useful to look at some of the relations that come out of these fundamental equations.
我们接下来可以考察,从这些基本方程中得出的一些方程。
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You've got to juggle the two equations, multiply that by 4, multiply that by 3, add and subtract and so on.
同时处理这两个方程,这个两边乘以4,另一个两边乘以3,将两方程相加或相减求出答案
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I want to show you how easy it is to change the code. But, notice, once I've added this I actually have a problem. This is now an under-constrained problem. I have more unknowns than I have equations.
我加上这个条件后,我马上面临一个问题了,这就是现在是一个非约束性问题了,我的未知数比方程数多,你从代数中可以知道。
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So now I've got actually, that looks like three equations, it's really just two equations, because one of them implies the other.
最后实际上是,看似三个方程,实则只有两个方程,因为其中一个暗示了另一个
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And, if you have trouble balancing equations, you can look in section 2.11 in the text.
如果你在配平方程式方面有问题，你可以看看课本中的2。11节。
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He speaks in a language of math and it is very important for students to be able to have hot copies so that they can take notes on the paper rather than be working very hard to copy down the equations that he used in these lectures.
他以数学语言授课,所以发给学生教学材料,是非常重要的,这样就可在纸上做笔记,而不用拼命,抄下他在课上,用到的等式。
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You can see the different points-- I've calculated this using data from 1983 until 2006-- and I computed all of the inputs to those equations that we just saw.
你可以观察不同的点-,我用从1983年到2006年的数据-,代入我们刚教授的等式,进行了计算。
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So, all you will have the opportunity to solve differential equations in your math courses here. We won't do it in this chemistry course. In later chemistry courses, you'll also get to solve differential equations.
你们在数学课中有机会,遇到解微分方程,我们在这化学课里就不解了,在今后的化学课程里，你们也会遇到解微分方程的时候。
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And we can do that by going through and deriving What we'll call the fundamental equations of thermodynamics.
通过推导,所谓的,基本热力学方程可以做到这一点。
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That is, in terms of equations of state. For any material Then we would really be able to essentially calculate anything. Anything thermodynamic.
换句话说，利用任何一种物质的状态方程,我们就能够实质上,计算所有物理量，所有热力学量。
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And I had mentioned several times thatyou do not need to memorize the majority of the equations and you don't need to memorize any physical constants.
另外我已经提过好几次了,绝大多数的公式大家都不需要去背,也不用去记任何物理常数。
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System of linear equations. What are the equations here? Well, I could say, you know, the number of pigs plus the number of 20 chickens equals 20, right? Because we've got 20 heads. And then what else do I have?
如何解决这个问题呢？,用线性方程式的办法来解决，等式是什么呢？你应该知道,猪的数量加鸡的数量等于,对吧？因为我们有20个头？
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Maybe you didn't realize that they are just simultaneous equations that you solve.
也许你并没有意识到,它们其实就是你们平时解的方程组
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Set the intersection points equal, the equations equal to each other and solve.
令交点处的两个方程相等,然后就可以解出来了
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So I have three equations and three unknowns.
现在我有了三个方程式和三个未知量。
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The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.
解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件
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And in terms of equations that we use, it's sometimes easier to plug in the fact, since momentum is equal to mass times velocity.
在我们使用方程这方面，事实上有时是很容易代入的，因为动量等于质量乘以速度。
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You'll also see that they have all the physical constants that you're going to need, and also a bunch of the actual equations that we've been using in the first couple weeks here.
大家还可以看到这里有,你可能会用到的所有物理常数，还有一堆公式,是那些我们这几周来一直在用的。
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Everything I told you last time, you can summarize in these two equations.
上节课上我所讲的所有内容,可以总结为这两个方程
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All it could do, though, was solve those equations.
它所能做的就是解决这些方程组问题。
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I want you to think for a second about two equations.
我希望你们仔细思考一下这两个方程
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You don't have to write everything in equations.
你没有必要把所有东西都写成方程式。
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But just to be really clear, I've written out exactly which equations you do have to memorize on the front here, so long as you know those, the rest you can just look up.
但是让大家清楚，我已经,把大家需要记住的公式都写在前面了，只要你知道了这些，其它的就只需要查了。
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And we can look at precisely why that is by looking at the equations for the energy levels for a hydrogen atom versus the multi-electron atom. So, for a hydrogen atom, and actually for any one electron atom at all, this is our energy or our binding energy.
而且我们可以精确地看看,为什么是这样的,通过看对于氢原子和,多电子原子能级的方程所以对于氢原子，事实上对于任何一个电子，这是我们的能量或者我们的结合能。
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We've done temperature, equations of state.
温度以及状态方程的概念。
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Newton. And he sent us on the road to understanding all the natural phenomena until the year 18-hundred-and-something when Maxwell invented the laws of electromagnetism and wrote down the famous Maxwell Equations.
他引领我们走上了探索自然现象之路,直到19世纪的某一年,麦克斯韦提出电磁学定律,并写下了著名的麦克斯韦方程组
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So the equations are very smart.
这些方程真的很神奇
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