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Literally, return the control from this function, and take the value of the next expression, and return that as the value of the whole computation.
正如字面意义上说的，从这个函数返回，然后取得下一个表达式的值,并把这个值作为整个计算的结果返回。
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How many steps does it take for this function to run? Well, you can kind of look at it, right?
这个方法运行了多少补？,你可以看看代码？
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And when we take the wave function and square it, that's going to be equal to the probability density of finding an electron at some point in your atom.
当我们把波函数平方时，就等于在某处,找到一个电子的概率密度。
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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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It then should take an argument or parameter if you want your function to take input.
然后它必须携带一个参数或参量,如果你想要你的函数获得一个输入。
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This particular one down here, this portion here is a heart/lung machine and this is a machine that can take over the function of a patient's heart and lungs during the period when they're undergoing open heart surgery, for example.
下面这是一个特别的设备,这一块是,心肺机,这台机器能够,在病人接受心脏手术的时候,替代病人的,心脏和肺的功能
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As we'll discuss in the class, and most of you probably know this, your body weight is a function of how many calories you take in and how many calories you burn off through metabolic processes but also physical activity.
我们将会讲到,而且你们中的大部分人可能也知道,你的体重随着卡路里的摄取量,和代谢中的消耗量而变化,还跟肢体活动有关
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So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。
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Change the independent variable, find the change in the function, take the ratio and that's the derivative.
改变自变量,算出函数的变量,计算比值,这就是求导
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One way to think about this intuitively if the derivative is very large the function is changing quickly, and therefore we want to take small steps.
关于这个方法很直观的一点想法是,如果导数非常大,函数也就变化的非常快，因此我们想一小步一小步的来。
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So, what we can do to actually get a probability instead of a probability density that we're talking about is to take the wave function squared, which we know is probability density, and multiply it by the volume of that very, very thin spherical shell that we're talking about at distance r.
我们能得到一个概率,而不是概率密度的方法,就是取波函数的平方，也就是概率密度，然后把它乘以一个在ｒ处的,非常非常小的,壳层体积。
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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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now we're not just talking about 1 photon, 1/2 let's say we shoot them all at the same time at our metal, each of them having some energy that's let's say 1/2 the work function. So, just to take a little bit of an informal survey, who thinks here that we will have an electron that is ejected in this case?
我们现在不仅仅讨论一个光子，它们所具有的能量是功函数的，我们在同一时刻把它们打到金属上,我们做一个不太正式的调查,谁认为这种情况下,一个电子会被打出？
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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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If I give you a function, you know how to take the derivative.
如果我给你一个函数,你就知道如何求导
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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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X So here I'm declaring another variable called X, and this is totally legitimate because I already know that if I'm implementing a function like swap or increment, I can absolutely take input.
这里我声明另一个变量，这个完全是合法的因为我已经知道,如果我执行一个像swap，或，increment的函数，我完全可以携带输入。
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Well, simply with the * notation at least on the way in when you declare the function called swap, you simply say this is not going to take an int and another int because that's useless.
好的，简单说，当你声明一个函数调用swap函数时,使用*符号，你可以简单说，这不能使用一个int数和另外一个int数,因为那是无效的。
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But as soon as the most recently called function finishes executing, you have to take that tray off the stack in order to get at the previous function's memory, and once he's done executing, you have to take that one off and then what's left well then main.
但是，一旦新的调用函数结束了执行,你必须从堆中把托盘拿掉,用来获得先前函数的内存，一旦他完成执行，你必须把那一块拿下来,然后剩下的是main函数。
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I would say, okay, this guy wants me to find a function which reduces to the number a when I take two derivatives, and I know somewhere here, this result, which says that when I take a derivative, I lose a power of t.
出题者想要我找出一个函数,它在经过两次求导后得到数字a,我知道这里的某个地方,这个结论告诉我,我每求一次导,t就降一次幂
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So let's just think exactly what this means, and that means that if we take away function and we define it in terms of n, l and m sub l, what we're defining here is the complete description of an orbital.
让我们来考虑一下这是什么意思，这是说如果我们不考虑波函数,而是用ｎ，ｌ，ｍ下标ｌ来定义它，我们定义的,是一个轨道的完整描述。
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Then, to find the meaning of b, we take one derivative of this, dx/dt, that's velocity as a function of time, and if you took the derivative of this guy, you will find as at+b. That's the velocity of the object.
接下来,为了弄清b的含义,我们取它的一阶导数,dx/dt,得到速度作为时间的函数,如果你对它求导的话,你会得到at+b,这就是物体的速度
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Now, I hope you guys know that much calculus, that when you take a derivative of a function of a function, namely v square over 2 is a function of v, and v itself is a function of t, then the rule for taking the derivative is first take the v derivative of this object, then take the d by dt of t, which is this one.
我希望你们了解更多的微积分知识,当你对复合函数求导时,也就是说v^/2是关于v的函数,而v本身是关于t的函数,求导的法则应该是,第一步是这一部分对v求导,然后v再对t求导,得到这一部分
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