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Here you've got a red light which doesn't seem to enter into this sense of the arbitrary and differential.
这里，红灯看起来并没有,任意性和差异性。
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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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This is a calculus-based class and I expect everyone to know at least the rudiments of differential calculus.
这门课需要微积分的数学基础,我觉得每个人至少应该知道,一些微积分的基础知识
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Small-cap stocks are tougher to price than large-cap stocks, so there's a 4.7% differential, first to third quartile.
小盘股比大盘股更难定价,第一和第三个四分位数的差距有4.7%
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Well we can go look up here, looking at the differential, there are no approximations here.
好的我们可以看这儿,看这个微分方程，这里没有做近似。
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So that what's new in Saussure's thinking about the relationship between signified and signifier is that the sign tied up in this relationship is both arbitrary and differential.
这就是索绪尔所贡献的了,能指和所指的关系,也就是符号的组成方式,是任意的，有差别的。
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MI stands for heart attack, myocardial infarction, and in this case you see an even bigger differential of people with a metabolic syndrome having even more elevated risk then they did for stroke.
I表示心脏病发作,心肌梗塞,在此可以看到患有代谢综合征的患者,比非患者心脏病发病风险更高
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OK, and now we return to this differential.
好，让我们回到这个微分式。
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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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Now we can use it to derive differential relations for all of the thermodynamics quantities.
现在我们可以利用他们,推导所有热力学量的微分关系。
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So the delta v here is an exact differential, but this dw is not.
你是如何,到达这个状态的。
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Not only did he formulate laws of gravitation, he also invented calculus and he also learned how to solve the differential equation for calculus.
他不仅找出了引力定律的公式,还发明了微积分,同时也得出了微分方程的解法
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Of course, in the venture capital world, the least efficiently priced of all, there's a 43.2% differential between the top quartile and the bottom quartile.
当然在最无法有效定价的风险投资领域,第一和第三个四分位数之间的差距,可以达到43.2%
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Arbitrary and differential are two correlative qualities.
任意性和差异性是两个相关的属性。
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When Modigliani and Miller wrote, there was a differential tax rate between dividends and capital gains.
莫迪利阿尼和米勒写到,如果在股利和资本收益间,有一个随其他因素变化的税率
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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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So the result is we can combine all of these as a single differential, and just like we've seen before, what that suggests is that we define another new quantity given by this expression.
结果就是我们能把所有的结果,整理成一个单一的微分，就像我们前面看到的一样，这说明我们可以利用这个式子,定义一个新的物理量。
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We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.
我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。
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So, let's say we start off at the distance being ten angstroms. We can plug that into this differential equation that we'll have and solve it and what we find out is that r actually goes to zero at a time that's equal to 10 to the negative 10 seconds.
也就大约是这么多,所以我们取初始值10埃,我们把它代入到,这个微分方程解它,可以发现，r在10的,负10次方秒内就衰减到零了。
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So signs are arbitrary-- and they're also differential.
所以符号是任意的，但是他们也是有差异的。
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The signs are both arbitrary and differential.
符号具有任意性和差异性。
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So we already know that. So now we can write CpdT or differential dH as Cp dT plus dH/dp, pdp constant temperature, dp.
我们已经知道了这个，所以我们现在,可以写出H的微分式：dH等于，加上恒温时的偏H偏。
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And this little slash here means an in inexact differential.
请注意这里的小横杠,说明这不是一个准确的微分。
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We can measure the heat capacity at constant volume, and now we have another term, and if we can figure out how to measure it, we'll have a complete form for this differential du which will enable us to calculate du for any process.
我们能够测量恒定体积下的热容，这里我们有另一项，如果能够知道怎么测量它，问我们就有了这个完整的微分式,就能够对任何过程计算。
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You won't have to solve it in this class, you can wait till you get to 18.03 to start solving these types of differential equations, and hopefully, you'll all want the pleasure of actually solving the Schrodinger equation at some point. So, just keep taking chemistry, 18 03 you'll already have had 18.03 by that point and you'll have the opportunity to do that.
你们不用在课堂上就解它，你们可以等到得到18，03之后,再开始解这些类型的微分方程，希望你们都想得到,实际解薛定谔方程的乐趣,所以，保持来上化学课，你们在那个点将会得到,你们有机会做到的。
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But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.
但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。
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