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

耶鲁公开课 - 基础物理课程节选

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。

I'm worried 实战 - SpeakingMax英语口语达人

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

So this is the central idea of calculus, right?

这是微积分的核心思想,对吗

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 基础物理课程节选

Okay, good. So we're going to use calculus.

很好,下面我们要用到微积分的知识

耶鲁公开课 - 博弈论课程节选

That's the meaning of the limit in calculus.

那是微积分学里的极限思想

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

That is the whole triumph of calculus is to know that by looking at the position now, the position slightly later and taking the ratio and bringing later as close as possible to right now, we define a quantity that we can say is the velocity at this instant.

这就得靠微积分了,通过了解它现在的位置,和一小段时间以后的位置,计算它们的比,再让时间间隔尽可能缩短,我们就定义了一个,被我们称之为瞬时速度的物理量

耶鲁公开课 - 基础物理课程节选

So, in the language of calculus, x is a function of time and this is a particular function.

所以,从微积分的角度来看,x是一个关于时间的函数,而且是个很特殊的函数

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 基础物理课程节选