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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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because then you can solve new problems on midterms and what not if you understand the conceptual part.
因为这样你可以解决中期的新的问题，如果你不理解的话，就不好说了。
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But in terms of SI units, which become much more useful if you're actually trying to use intensity in a problem and cancel out your units, we're just talking about joules per second is what intensity is.
但是用国际单位制，这个变得越来越有用了,如果你实际上在使用强度,来解决问题和约化单位，我们仅仅讨论每秒钟的焦耳,这就是强度。
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STUDENT: So, how do you come to a conclusion as to which you should use then, if you can determine the size based on solution, or based on input, so how do you decide?
学生：所以，你怎样决定你该用,哪个来算呢？现在如果你可以选择是，基于解决方案的大小，还是基于输入的大小，你应该怎样决定呢？
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That will be--No, not at me, at each other, and that will be the person If you are unable to resolve this dispute yes, you two, please--if you are unable to resolve this dispute, the person to the right of me will be the smiler.
这将是，不，不是我，互相看，将是这个人,如果你不能解决这个争端的话,对，你们俩，请，如果不能解决，我右手边为微笑方。
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If you can do this, you can do most of the problems you will run into.
如果你会做这个,那么你就能解决碰到的大部分题目了
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But if you can accept the purity of the statement I just made, it is at the root of the thing you have a solution.
但如果你能够遵从原教旨主义的方式,那么这就是你解决此问题的根本
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You can take a problem that might be relatively intuitive to solve but when you scale this thing up as is increasingly the case in the web, in large data systems, and so forth, you actually have to now think smart, you actually have to think efficiently and you have to solve this problem effectively.
你可以把一个问题用比较直观的方法解决,但如果你把此类问题的数量增大,正如越来越多的互联网，和大规模数据系统中出现的问题等等,你应该考虑怎样才能更简便，怎样才能更高效,你应该用行之有效的方法处理问题。
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When you have difficulty creating your own work, how do you deal with it?
如果创作碰到障碍了，你如何解决呢？
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Let's quantify the energy value. If you go through and solve for energy, you will get this equation.
我们来确定一下能量值，如果你试图寻找,解决能量问题，你能得到一个方程式。
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Ask yourself, will it fix all of the symptoms you've seen?
你第一个想到的修改方案,它能否解决你看到的所有症状？如果不行？
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It's definitely an opportunity for help, but particularly, as an opportunity to work with someone for just a few moments to help get you unstuck or to get you past some stumbling block that, otherwise, if you struggled with on your own, you might sink or waste even multiple hours on just something that you're not seeing.
这是一个寻求帮助的机会，特别是，作为一个与某人一起工作的机会,他们能帮助你解决问题,或帮助你越过绊脚石，否则，如果你自己单独奋斗，你可能,浪费很多时间在,你不了解的东西上。
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So it turns out there's a solution to this: If you need more precision, more digits after the decimal point than a float allows, what do you go for instead?
所以这里有一个解决方案：,如果你需要比float类型允许的更高精度，小数点后更多位数,那你该用什么取代它？
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> David: Yes, if you really, if you want to reimplement the solution from last where whereby it was buggy, you can absolutely say take the address of x then go there, thereby undoing all of the work you just did.
>，大卫：是的，如果你的确，如果某个地方有bug，你想要重新,实现那个解决方案，你绝对可以通过x的地址，定位到那里去，然后撤销你刚做的所有工作。
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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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The problems are set up so that, if you start down the right path, it should be pretty straight-forward to work it through If you start down a plausible but incorrect path, you can sometimes find yourself stuck in the weeds somewhere, and we want to bring you back in.
问题提出了，如果你从，一开始就走正确的道路，解决的途径,就一目了然了,如果你走上一条貌似正确但实际错误的道路，你会在某时某刻,发现自己陷入泥沼，于是我们就会把你拉回来。
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And she would intercept them as they came across the rickety bridge, or the low bridge, and she would ask them a few questions and ?" conclude with, "Can you write me a story? " You would help me out with my experiment if you'd just write a little story right now."
她会拦住他们,当他们分别横过摇晃的桥和低矮平稳的桥时，她会问一些问题,最后一个问题是“能为我写一个故事吗“,我将解决实验中遇到的瓶颈,如果你能立即给我写一个小故事“
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You're not going to start for the rest of your life if you ever need to solve a problem with a computer from scratch, odds are you're going to reach for some off the shelf packages or libraries or tools that other people wrote so that people like us don't have to reinvent the wheel again and again.
如果你想用Scratch来解决问题,却使用其他人写的程序,或者利用现成的资料或工具,这样以来,我们的确可以避免做重复性的工作,但却永远学不会编程。
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