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Now Isaac Newton and/or Joseph Raphson figured out how to do this kind of thing for all differentiable functions.
既然牛顿和拉复生已经,指数了如何解这种可导函数,因此我们就不用太担心了。
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So what they do is, they're describing how these thermodynamic properties change, in terms of only state functions and state variables.
他们的作用是描述,随着状态函数和状态变量的变化，系统的热力性质如何变化。
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Gas phase single atom. So we don't have to deal with work function or any kind of energies associated with some condensed form of matter.
气相的单原子，所以我们不需要再,处理功函数的问题,以及和凝聚态相关的能量问题。
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So when you operate on the wave function, what you end up with is getting the binding energy of the electron, and the wave function back out.
所以当你将它作用于波函数时，你得到的是电子的结合能,和后面的波函数。
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It turns out there's a new function strlen S-T-R-L-E-N that you probably have not used yet called strlen, S-T-R-L-E-N, programmers early on and still like to be succinct but communicates sufficiently what they mean.
结果这里有个新的函数,你可能没有使用过，叫做，早期的和现在的程序员喜欢简洁地,但是能充分的传达他们的意思。
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Square root of 16, and my plot basically shows it crosses at 4 and-- well, I think that's minus 4.
我的图清楚的显示这个函数,在4和-4两个点和x轴交合。
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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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So here's Player I's payoff as a function of what Player II chooses and what Player I chooses, so we have that already.
这个就是参与人I的收益的方程,它是参与人I和II策略的函数,我们已经得到了
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It's a state function, so we're at constant temperature and pressure, and now we want to consider some chemical change or a phase transition or you name it.
这就是态函数，我们处于恒定的温度和压强之下，然后考虑某些化学变化或者相变,或者你想考虑的东西。
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But this choice of names, both for my functions and also for my parameters or my variables is completely up to me.
但是这个名字的选择，包括我的函数名,和我的参数名,或者变量名都是我定义的。
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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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so, remember we can break up the total wave function into the radial part and the angular part.
记住我们可以把整体波函数,分解成径向部分和角向部分。
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And then I could also do a Gaussian one here, with the mean of and the standard deviation of volatility divided by 2.
然后我在这里再写一个高斯分布的函数，它的浮动值的平均值和,标准偏差值都除了2。
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So we do, in fact, have a dependence on what the angle is of the electron as we define it in the orbital.
实际上当我们定义电子在这个轨道,它的波函数的确是和角度有关的。
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Similarly for G as a function of temperature and pressure, I can go through the same procedure.
同样的G作为,温度和压强的函数，我可以采用相同的步骤。
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So let's actually see how we solve this with this function with actual code.
然我们看看怎样用,这个函数和代码解决这个问题。
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In particular functions that operate on the data, perhaps on other data as well. The key idea here is to bind together the data and the functions that operate on that data as a single thing.
特别是处理数据的函数，也可能处理其他数据,这里的关键思想就是,将函数和操作数据的函数。
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s We are back over to E as a function of n, l, m and s, only we got there through this other torturous route.
我们回到将E作为函数n，l和，只要我们解决了这个烦人的路径。
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You have to with C, as with a lot of programming language, say what you return.
在C语言和大部分语言中,你必须说明函数的返回值。
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In other words, your job is to guess a function whose second derivative is a, and this is called integration, which is the opposite of differentiation, and integration is just guessing.
换言之,你的任务是要猜出一个二阶导数为a的函数,这就是积分,和微分恰恰相反,积分就是猜
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So, as an example, let's take argon, I've written up the electron configuration here, and let's think about what some of the similarities might be between wave functions in argon and wave functions for hydrogen.
所以作为一个例子我们来看看氩，我已经把它的电子构型写在这里，我们来考虑氩和,氢波函数之间的,一些相似性。
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There's been a lot of work done on these over the years, but in fact, it's pretty hard to invent a good hash function. So my advice to you is, if you want to use something was a hash, go to a library. Look up a good hash function.
已经做过了很多的尝试和努力,但是事实是，很难发明出一个好的哈希函数,所以我给你们的建议是,如果你们想使用哈希功能,到函数库中查找一个好的哈希函数。
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So, you remember from last time radial nodes are values of r at which the wave function and wave function squared are zero, so the difference is now we're just talking about the angular part of the wave function.
你们记得上次说径向节点在,波函数和波函数的平方,等于零的ｒ的处，现在的区别是我们讨论的是,角向波函数。
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An object is a collection of data and functions.
对象就是数据和函数的集合。
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We want to do the same thing, but with our data types.
我们想要创建数据类型和函数，或者我们会叫他们方法。
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R And we abbreviate that by calling it r, l by two quantum numbers, and an l as a function of little r, radius.
我们把它简称为，两个指定的量子数n和，它是半径小r的函数。
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In general, temperature and volume or pressure.
一般来说写成了温度，体积和压强的函数。
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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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And just as with variables, you should use some common sense, some style here, and the function's name should X Y communicate what it does, calling it X or Y or Z is generally not all that helpful.
就像变量，你使用一些常识，一些类型，和函数名需要,传达它所做的事情，把它叫做,或者Z通常是没有什么用处的。
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So even though increment is obviously increment declared and defined in this function, it's later; so it's too late for me to use it in main.
很明显，即使在这个函数中,已经声明和定义;,也太迟了，以至于，我在main函数中不能使用它。
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