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The math quiz is on calculus, and I am really bad at it.
这次数学考试是关于微积分的，是我特别不擅长的部分。
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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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All I did was, I did a little bit of calculus, a little bit of algebra, and then I drew the thing.
我只不过是稍微用了点微积分,做了点代数运算,然后就画出来了
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Because what matters is where they are in the power calculus.
因为重要的是,他们在整个权力体系中居于怎样的位置。
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Suppose the utilitarian calculus in the long run works out as he says it will such that respecting people's rights is a way of making everybody better off in the long run.
假设如他所说，长远来看,功利主义演算真能实现,即尊重个人权利,从长远来看，真的能让大家都获益。
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Emotion ruled the decisions, not rational economic calculus.
情绪主导了投资决策,而不是理性的经济学计算
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I got the feeling, when I was talking to some of you guys, that maybe you should brush up on your calculus.
当我和你们中某些人聊天时,我感觉到,你们应该好好复习微积分
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So I'm going to find for you this result using calculus in a different way.
我将为你们展示,用不同数学方法得到的结果
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We did something very nerdy, namely, we just played with calculus and algebra.
我们使用了些死板的,微积分和代数
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I think you guys know enough calculus for me to write.
你们的微积分水平应该能允许我直接写出来
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I want to do this carefully and slowly, and before I even start, let me point out in passing that calculus is not going to help us here.
我要慢点仔细讲这部分,在我开始之前,我需要说明微积分,在这里是用不着的
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How many of you remember this from when you were high school calculus days or from 112?
多少人还记得高中微积分的知识,或者还记得112的课程内容的
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For people whom that didn't mean anything, it doesn't matter. We're not going to calculus today.
那些不了解微积分的同学,不必担心,我们今天不会用微积分
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We'll probably try and line up a quick calculus lesson, a special section for those people.
我可能会开一个微积分速成班,专为没学过微积分的人准备
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So, I will remind you, again, this is not a course in calculus.
我要再次提醒你们,这不是微积分课
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Not even calculus, all you need is high school.
丝毫不需要微积分,高中数学知识足矣
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So this is the central idea of calculus, right?
这是微积分的核心思想,对吗
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Everyone knows from calculus that if you're trying to find a function about which you know only the derivative, you can always add a constant to one person's answer without changing anything.
学过微积分的人都知道,如果你想根据已知的导数,求出其原函数,你总是可以给某人的答案,随便加一个常数,且不影响结果
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Now, we get to draw some lessons out of this thing, so everybody who's feeling a little bit shell shocked from having been doing algebra and calculus and drawing pictures and feeling like they've been cheated into taking a class that looks far too much like economics, calm down we're going to actually talk right now.
下面我们从中总结点经验出来,那些因为代数和微积分计算还有绘图,而感到十分不爽的同学,你们是不是感觉被我忽悠了,才会选这门一点都不像经济学的课啊,稍安勿躁,我们马上切入正题
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I am hoping that if you learned your calculus, you learned about derivatives and so on by looking at x versus t.
我希望你们学习微积分时,通过观察x-t图来,学习导数等内容
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Now you have to know from elementary calculus that v times dv/dt is really d by dt of v square over 2.
根据初等微积分知识你们得知道,v乘以dv/dt其实就是d/2)/dt
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You've got to realize that in calculus, the symbols that you call x and y are completely arbitrary.
你应该明白在微积分中,选x还是y当符号是完全任意的
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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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There is a chapter in the back of the book, I think it's chapter 25, that goes over this, it refreshes your memory of such calculus.
课本的后面有一章,我记得是25章,会涵盖这些内容,你们可以去重温一下微积分
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Or do you think this completely destroys the whole utilitarian calculus?
还是你们认为它完全推翻了,功利主义的演算？
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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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But I showed you in the end how we can use calculus to derive that.
我上节课最后教过你们,如何用微积分来得到那个结果
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If you have not seen the calculus that I'm about to use on the board, or more likely, if you've forgotten it since high school, don't panic.
如果你们没有见过我将要,在板书上写的表达式,或者说,高中毕业你们就忘了,没关系
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I want to derive the last result in another way, then I will stop, and that's pretty interesting because it tells you the use and abuse of calculus.
让我用其他方法解答最后一个问题,然后今天就到这 这是一个挺有意思的题,因为它展示了微积分的正确用法和错误用法
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