One night, Amanda was chatting on the Internet while Jennifer did her calculus homework.
有一天晚上詹尼佛在写微积分作业，阿曼达则是上网聊天。
And, just to motivate that, let me remind you about one trick that you probably know from single variable calculus, namely implicit differentiation.
作为引子，你们可能已经知道了，一元微积分里面的一个小把戏，也就是求隐函数微分法。
Very good. OK, that's at least one thing you should remember from single variable calculus.
非常好，这是一元微积分中，你们至少应该记住的。
However, we'll see one later using a cool trick, and multi-variable calculus. So, for now, we'll just leave the formula like that, and we don't know how long it is.
但之后我们会用很酷的方法解决它，以及多元微积分，但目前，我们只需要写到这就行了，我们还不懂如何计算它。
He was a brilliant mathematician; he was one of the inventers of Calculus.
他也是一位杰出的数学家，微积分的发明者之一。
For if these increases of income or utility are reduced to being infinitesimal, one can use both the symbolism and the powerful manipulations of the differential calculus.
因为，如果这些收入或效用的增加可以化为无穷小，那我们既能使用符号表示，也能利用微分学强大的操作了。
There are now 3000 students participating in the CS study group, 2400 in the calculus study group, and 800 in the Chinese one.
现在有3000名学生参加科学计算机课程的讨论组，微积分组有2400人，而在汉语基础组中有800人。
It is the same thing as, in one variable calculus, when you take the anti-derivative of a function it is only defined up to adding the constant.
相当于在一元微积分中，取一个函数的不定积分，仅仅需要在结果后加一个常数。
This is just one striking instance of the immensity of pain in the animal kingdom, which defies explanation except via the unyielding calculus of competitive survival.
在只是动物王国的一个简单的寄生的例子罢了，这个从另一个方面证明了不用竞争也可以生存。
I, for one, could not teach chemistry to my children but I could probably teach them calculus.
对于我自己，不能教给他们化学，但是我可以教他们微积分。
Abstract: : the limit is Paramount basic concept in calculus, but also is one of the foundations to establish and apply all kinds of calculation methods and related concept in calculus.
摘要：极限是微积分中至为重要的基础概念，也是建立及应用微积分学中各种计算方法、相关概念的基础之一。
It begins with the properties of the real Numbers and continues with a rigorous treatment of sequences, series, metric Spaces, and calculus in one variable.
它从实数的特性开始并且继续严格的处理顺序，系列，米制空间和在一个变量的微积分。
But I when the only second choice would be the Calculus, which one should I choose?
但是当唯一的第二选择是微积分的时候，我该选哪个？
As the base of high mathematics, differential and integral calculus for function of one variable has the direct influence on the training of students mathematics attainment.
一元函数微积分学是高等数学的基础，直接影响学生数学素养的培养。
But then at least see calculus as one of the tools essential for mastering your subject and see it as the theory which teaches you how to attack and solve problems in a systematic way.
但至少把微积分看作是掌握学科的重要工具，而且是教你学习如何有系统地进攻与解决问题的重要理论。
Before I learned it it sounded like one of the hardest things in the universe right up there with quantum mechanics. Quantum mechanics is still beyond me but calculus is nothing.
在我学习它之前，它听上去好像是世界上最难的一件事，好像和量子力学差不多。
The indefinite integral calculation is one important sector in calculus.
在大一的数学教学中，不定积分既是一个重点也是一个难点。
Rolle's theorem plays a very important part in the study of one differential calculus. This paper attempts to explore the application of Rolle's theorem from the perspective of constructing function.
罗尔定理在一元微分学处于很重要的地位，本文通过构造函数的思想来探究罗尔定理的应用。
Rolle's theorem plays a very important part in the study of one differential calculus. This paper attempts to explore the application of Rolle's theorem from the perspective of constructing function.
罗尔定理在一元微分学处于很重要的地位，本文通过构造函数的思想来探究罗尔定理的应用。
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