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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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You and your partner, Warren Buffett, have for years complained and warned about the dangers ve perceived in the modern derivatives markets, particularly credit derivatives, and also concerns about interest rate swaps, currency swaps, and equity swaps.
你和你的合伙人，沃伦，巴菲特,多年来一直提醒现代衍生品市场中,存在的危险，that，you’,尤其是信用衍生品，利率掉期，货币互换和股票互换。
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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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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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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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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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In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.
换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。
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You can easily check by taking two derivatives that this particle does have the acceleration a.
你可以很容易地通过求两次导来验证,这个质点的加速度确实为 a
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This way when I take two derivatives, there will be no t left.
这样的话,当我求二阶导数时,t就消失了
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I'm going to write the particular case of R and take derivatives.
我会写出 R 的一个特例,然后对其求导
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The most important result from last time was that if you took this r, and you took two derivatives of this to find the acceleration, d^2 r over dt^2, try to do this in your head.
上节课最重要的结论,就是如果你把 r 写成这样,对 r 求两次导就能得到加速度,d^2 r / dt^2,心算一下
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It's constant pressure. OK, so now, last time you looked at the Joule expansion to teach you how to relate derivatives like du/dV.
这是恒压的，好，上节课你们,学习了焦耳定律,以及怎样进行导数间的变换。
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You can actually take derivatives of a vector with time.
你可以直接求位矢对时间的导数
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Just take the derivatives and that's the velocity vector.
直接计算对时间的导数就是速度矢量
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We want to get rid of derivatives.
我们对两边。
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i and j are constant, ignore them when you take derivatives.
和 j 是常矢量,求导的时候可以忽略它们
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So, the point is whenever you have derivatives with something over dt, do not hesitate to cancel the dts This will be actually true as long as both quantities are vanishingly small.
关键在于,只要你推出的式子分母上有dt,不要犹豫,直接约掉,这个式子只在,两遍都是无穷小的情况下成立
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