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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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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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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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How many of you, we won't let the camera see you, how many of you have not I'm not going to show hands at all.
多少人,摄像机先别拍他们了,多少人没有学过微积分,请大家举手吧
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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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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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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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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 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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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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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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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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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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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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We're going to use calculus of one variable.
我们只用单变量微积分的知识就够了
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Okay, good. So we're going to use calculus.
很好,下面我们要用到微积分的知识
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That's the meaning of the limit in calculus.
那是微积分学里的极限思想
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You really have to know calculus.
你们必须真的懂微积分
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You have done it before, but when you say, "I know calculus, " Sometimes it means you know it, sometimes it means you know of some fellow who does or you met somebody who knows.
你们以前学过,但当你们说,"我懂微积分",有时这表明你们懂,有时表示你知道谁懂,或者你遇到了懂这个的人
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I think that book will give you all the basic principles you need in calculus of one variable, more variables, elementary complex numbers, maybe solving some problems with vectors and so on, which you're going to get into.
我想那本书会给你所需的所有基本知识,包括一元和多元微积分,简单的复数运算,可以解决一些与矢量有关的问题,而这正是你们将要学的
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