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The CME Group, operator of the Chicago Mercantile Exchange, is one of the world's largest traders of derivatives.
VOA: special.2011.02.18
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This should be particularly bothersome to you because, as you've already experienced in 5.60, There are a lot of partial derivatives.
对你们来说这可能很让人头疼，就像你们在5。60里体验过的那样，这有很多偏微分和变量。
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And what's fallen out when we do that, because in each case, one of the first derivatives gives us the entropy.
当我们这样做时就得到了结果，因为在这些例子中，一阶导数是熵。
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The largely unregulated market in derivatives is estimated at six hundred trillion dollars.
VOA: special.2010.04.16
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But then having found one answer, you can add to it anything that gets killed by the act of taking derivatives.
一旦你算出了一个答案,你就可以往式子里加入任何,在求完导后消失的项
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Both measures in Congress call for a system to supervise derivatives.
VOA: special.2010.04.16
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So here I've written for the hydrogen atom that deceptively simple form of the Schrodinger equation, where we don't actually write out the Hamiltonian operator, but you remember that's a series of second derivatives, so we have a differential equation that were actually dealing with.
这里我写出了,氢原子薛定谔方程的,最简单形式，这里我们实际上,没有写出哈密顿算符,但是请记住那你有，一系列的二次导数,所有我们实际上会处理一个微分方程。
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Highlights of the reform package include tougher regulations of financial derivatives and securities, along with a $50-billion bailout fund, to be paid for by banks.
VOA: standard.2010.04.19
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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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So I'm hoping you guys are comfortable with the notion of taking one or two or any number of derivatives.
我希望你们,能习惯求一阶,二阶,或者任意阶导数的概念
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So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.
我现在所要做的一切就是,考察自由能对,温度，体积和压强的偏导数。
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What's a function, what's a derivative, what's a second derivative, how to take derivatives of elementary functions, how to do elementary integrals.
什么是函数,什么是导数,什么是二阶导数,如何对初等函数求导,如何进行初等积分
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Now, I want to do one concrete problem where you will see how to use these derivatives.
现在我要解决一个具体的问题,从中你会明白如何运用这些导数
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It's three different second derivatives in terms of the three different parameters.
它是用三个不同常数表示的,三个不同的二阶导数。
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But, of course, it's going to come from the fact that these second derivatives are also equal.
但是，结果同样是依赖于,二阶混合偏导数相等。
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When you say that, it implies that the differential is given by this pair of partial derivatives.
这就意味着，内能的微分,等于偏u偏T，保持体积不变。
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Of course, you can take a function and take derivatives any number of times.
当然,你可以随意拿一个函数,对它求任意阶的导数
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Then you're supposed to know derivatives of simple functions like sines and cosines.
你应该知道一些简单函数的导数,比如正弦函数和余弦函数
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Because these mixed second derivatives are the same thing.
因为这两个混合二阶偏导数,是相等的。
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If I gave you the location of a particle as a function of time, you can find the velocity by taking derivatives.
如果我给出物体的位移是时间的函数,你可以通过求导来得到速度
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Rule for taking derivatives, if you want to do this mindless application of calculus, you can do it.
按求导法则来做,如果你想解决这个微积分的简单应用,你可以很容易做到
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Normally, I will give you a function and tell you to take any number of derivatives.
通常情况下,我会给你一个函数,然后让你求任意阶的导数
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If you're taking two derivatives you can add a constant and something linear in t.
如果你要二次求导,你可以添加一个一次项和常数项
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If you took the two derivatives of this guy, In other words, Same thing there.
对这一项求两次导,也就是说,这里也是一样
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But I can add to this some number, like 96, that'll still have the property that if you take two derivatives, you're going to get the same acceleration.
但是我可以在后面加上某个数,比如96,经过两次求导你仍会得到,同样的加速度
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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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But more and more vectors can be manufactured by taking derivatives.
但是更多的矢量,可以通过求导得到
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We can start taking derivatives of this with respect to time.
我们首先来对时间求微分
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Interestingly, only the first two derivatives have a name.
有趣的是,只有前两阶导数有名字
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Once you can take one derivative, you can take any number of derivatives and the derivative of the velocity is called the acceleration, and we write it as the second derivative of position.
只要你能求一阶导数,你就能求任意阶的导数,速度的导数被称为"加速度",我们把它写成位移的二阶导数
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