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"The field commander has said 'I need a lot more troops.' And I think it's more than most people, at least in their calculus in the back of their minds, imprecise as that probably was, it was a larger number than they were prepared for,".
VOA: standard.2009.10.16
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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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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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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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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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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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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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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 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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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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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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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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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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That means, when I take two derivatives, I want to get a, then you should know enough calculus to know it has to be something like at^, and half comes from taking two derivatives.
也就是说,当我想求二阶导时,得到了a,你应该有足够的微积分知识,才能知道必须有类似at^的项,而这个1/2则是因为求了两次导数
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I've found Player 2's best response as a function of q1, and the way I did it, just remember, the way I did was I applied a little bit of 112 and high school calculus, so that's your single variable calculus.
以及参与人2的最佳对策是q1的函数,而且我们用到的数学知识,只是稍微与112和高中微积分有关,仅仅是单变量微积分的知识
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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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