I mean, in this form, actually it's the same statement as in single variable calculus.
我指的是，在这种形式下，它和一元微积分的表述是一样的。
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。
Let's say that you want to understand actually all these rules about taking derivatives in single variable calculus.
如果说你要知道，关于一元微积分中所有的求导法则。
When you compute an integral in single variable calculus, you don't do that. You don't cut into little pieces and sum the pieces together.
当计算一个单变量的积分时，你不会这样做的，不会分割出一个个小块，再对这些小块求和。
Well, I don't expect that you would need integration by parts, although I still hope that some of you remember it from single variable calculus.
不要求掌握分部积分公式，但还是希望，有些人能在单变量积分中记住它。
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。
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。
OK, so, yeah that's a strong suggestion that if you've forgotten everything about single variable calculus, now would be a good time to actually brush up on integrals.
我强烈建议,如果你忘记了单变量积分的知识，现在就是一个很好的复习机会。
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。
You may want to note that this is the first volume, and that the second volume is also worth getting: Calculus, vol. 2: Multi-Variable Calculus and Linear Algebra with Applications.
你会发现这是他它的第一卷，并且第二卷也值得去读：微积分卷2：多远微分与与线性代数及其应用。
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。
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。
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。
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