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Now, we are very gentle in this course with respect to knowing integrals, but this is one you have to know.
这门课对积分,的要求并不高，但这个积分你们必须会算。
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which I don't know if it's a talent. But, if people enjoy it...
我不知道这算不算有才。但是，如果人们喜欢这个……
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You can go ahead and use that equation, or you could figure it out every time, because if you know the total number of nodes, and you know the angular node number, then you know how many nodes you're going to have left.
你们可以直接用这个方程，或者每次都自己算出来，因为如果你们知道了总的节点数，又知道角向节点数，就知道剩下的节点数是多少。
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du, it's an ideal gas. So this is Cv dT and of UB course we can just integrate this straight away.
因此这是CvdT，当然我们可以,直接算出这个积分，那么△
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How do I figure that out? Well I'm looping down the list, right? I'm walking down the list.
怎么算出来的呢？我在循环遍,历这个列表对吧？那要遍历这个列表。
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The total energy of the system, which we are going to get from postulate number four, which says the energy of the electron, which is the energy of the system, is the sum of the kinetic and the potential energy.
这个系统的总能量，也就是我们将从第四个假设中算出的能量，也就是电子运动产生的能量，也就是整个系统的能量，是动能和位能的总和。
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Not to harp on the mathematical features of this, but cubing, AX*X*X you know, if you're starting to do AX star, X star, X, every time you want to cube some value in a program, it just feels like this is going to get a little messy looking, if nothing else.
不要总是说这个的数学特性，但是体积，你们懂的，如果你开始做，在一个程序中，每次你想算几个数值的体积，感觉它就变得,有一点凌乱的，如果没有其他的。
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Then to get the monthly payment, you take the square bracketed thing and you divide by the mortgage balance and that's the monthly payment; that's how it's calculated.
如果要算每月偿还额,你用贷款余额,除以这个方括号的值,这样就得出每月偿还额,这就是每月偿还额的计算方法
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Those are not necessarily bad reasons to take this course, and with the exception of the sex part, this course might actually help you out with some of these things.
作为选择这门课程的理由,这些倒也并不算太差,当然除了性这个方面,这门课实际上还是能够帮助你们,解决一些问题的
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John? -You know I'm not gonna forecast ... either of those right now. -You are not gonna... I have the Taylor rule on the line with respect to the Federal fund's rate.
约翰呢？，-我现在不会,对这个做任何预测，-你不打算。,网上有泰勒规则啊,根据它能算出联邦基金利率。
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In addition, this is just the cost of the vaccine, not the cost of the doctor or nurse who injects it into, you so you have to figure that cost in as well.
另外,这个仅是疫苗本身的成本,还没算上医生或者护士的成本,所以你还得同时考虑这些成本
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But a few bits of jargon are going to be helpful in allowing the conversation to move forward and this is certainly one.
不过稍微懂一点术语,会让交流更顺畅,这个定义当然算术语
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Once you got a = 2, you can go back and realize here that f = 4, so you got really 4 Newtons.
一旦你算出 a = 2,你可以回到上面来,求出 f = 4,所以实际上这个力有 4 牛
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STUDENT: What does it mean, the operator used, when you were calculating the remainder between nine and five?
学生：这是什么意思，当你用这个运算符去算,9除以5的余数的时候？
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The algorithm doesn't know that it's going to take this long to compute, it's just busy crunching away, trying to see if it can make it happen.
这很可能会发生，但是你知道的,算法本身并不知道，计算这个问题需要多长的时间，它就一直忙碌的算啊算。
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And for any of the other compounds. So in other words, by defining that reference state, we can then figure out or measure heats of formation of a vast number of compounds.
对吧？对于任何其他的,化合物也是一样，所以换句话讲，定义了这个参考状态,我们就能算出或测量许多。
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So I'm going to show you a little trick for figuring that out.
因此接下来我会给你们讲一个,算出这个来的小把戏。
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If you have a bond with an interest rate of 4.375% -that's not an easy one to divide by two but you would get half of that every six months until maturity.
如果你持有一种利率为4.375%的债券,这个数除以2有点难算,而在债券到期前,每半年你能得到4.375%一半的券息
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And h with the carrot or the hat here, well, that carrot or hat tell us it must be an operator, and this is called the Hamiltonian operator.
而且带帽的H，好，这个帽告诉我们它肯定是一个算符，这个被称为哈密顿算符。
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We can look at the 2 p, which should have one radial node, and we just figured it out for the, excuse me, 3d for the 3 p has one radial node, and for the 3 d here, we should have zero radial nodes, we just calculated that.
我们看2p，它有一个节点，我们已经知道对于，不好意思，是3p有一个节点，对于，它应该没有径向节点，我们刚刚算过这个。
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Let's just... We'll get there, just to remind you, the way we read this is you give me a quantity of Firm 2, I find Firm 1's best response by going across to the pink line and dropping down.
我们当然也能算出来,提醒一下各位,这个图像的个意思是任意给出公司2产量,然后通过这条粉色的线,就可找出与之对应的公司1的最佳对策
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Now, we are done because now we can ask how high does it go, and you go back to your y of 1 is 15+10-5, which is what?
现在问题解决了,因为我们可以算出,最高点的高度,你回到这个式子,求出y=15+10-5,是多少
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As a matter of fact, it costs an increasing amount to play the game when you look at the fees that are paid to investment managers and hedge funds.
事实上,当把付给投资经理,和对冲基金的费用都算进去的话,这个博弈的成本越来越高
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It happens. Fortunately, while sitting in jail awaiting trial, the slow thief decided to figure what was wrong. And, amazingly enough, he had studied mathematics. And had a blackboard in the cell. So he was able to work it out.
失主叫了警察然后小偷最后被抓进了监狱,幸运的是这个贼做来牢房里,等待判决时发现了自己的错误,它很惊人的学习过数学，牢房里,还有一个黑板，它可以把题目算出来了。
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What q2 makes this equal to 0 and Katie's answer is solving out the algebra here is that q2 that solves this must be a - c over b.
2为何值时这个算式等于0呢,凯特回答其实就是算出这个的解,即,q2=/b
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It also tells you that if you compress the spring, compress it means x is now-- x is measured from this position, where the spring is neither compressed nor expanded.
它还能告诉你,如果压缩弹簧,压缩就意味着现在 x...,x 是从这个位置开始算的,在这个位置弹簧既没有压缩也没有伸长
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Iron as an element is a solid. That's it's most stable state at room temperature and pressure, right, and so on. And then we can figure out heats of formation.
铁单质是固态,这是他在室温和常压下,最稳定的状态，然后我们,可以算出生成热，现在这个。
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We want to have that definition clear because in fact we're going to, we might want tabulate heats of reaction, right, and of course want to know what the conditions are for the tabulated values apply. And we're going to want to calculate them from other quantities and again, we're going to need to know each case what are the relevant conditions?
我们想要明确这个定义,因为实际上我们会想把,反应热制成表格，当然我们会,想知道表中的数据在什么样的,条件下是有效的，我们会,想要从其他的量中算出它们,再一次，我们需要知道,每种情形下相关的条件是什么？
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We also know how to figure out the energy of this orbital, and we know how to figure out the energy using this formula here, which was the binding energy, -Rh which is negative r h, we can plug it in because n equals 1, so over 1 squared, and the actual energy is here.
我们知道如何算出,这个轨道的能级，而且我们知道如何,用这个公式,算出能量，也即是结合能，等于，我们把n等于1代进来，所以除以1的平方，这就是能量。
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And conceptually, the idea of cubing a value feels like you could package that up into a little box, a little tool that takes input, a value, and returns output the answer A* so you don't have to constantly do A star, A*A So this program ,at the end of today, is pretty much the same thing.
概念上，算一个值的立方就像是,你可以把一个值打包放在一个小盒子里,一个用来接收输入的工具,一个值，然后返回一个答案,所以你并不需要一直使用，等等。，A，star，，A，，and，so，forth。,这个程序，最后，是一个差不多的东西。
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