Now Isaac Newton and/or Joseph Raphson figured out how to do this kind of thing for all differentiable functions.

既然牛顿和拉复生已经,指数了如何解这种可导函数,因此我们就不用太担心了。

麻省理工公开课 - 计算机科学及编程导论课程节选

So let's understand: what is the nature of exponential function so that we can understand the power of one?

让我们先理解指数函数的本质,以便理解“一“的力量？

哈佛公开课 - 幸福课课程节选

And you really, wherever possible, want to avoid that exponential algorithm, because that's really deadly. Yes.

比你的电脑的性能增长的快多了，并且大家无论何时，都要避免去用指数级的函数。

麻省理工公开课 - 计算机科学及编程导论课程节选

e The charge on the anion times minus e, so there is the minus e squared, 0R0 and divided by 4 pi epsilon zero r naught, because now I am evaluating this function at r naught, one minus one over n where n is the Born exponent.

阴离子的电荷乘以，因此会有-e的频繁，除以4πε,因为现在我用r圈评估这个函数，1-1/n，n是波恩指数。

麻省理工公开课 - 固态化学导论课程节选

Or just have the good intentions without the effort that's necessary to bring about a positive exponential function.

还是只有好的意图但不付出,必要的努力发挥正面指数函数的作用。

哈佛公开课 - 幸福课课程节选

Because in "Pay it Forward", they capture this very idea of human networks as exponential functions.

电影“让爱传出去，深刻地描述了,人类网络是指数函数的观点。

哈佛公开课 - 幸福课课程节选

All right. The question is, is there a point where it'll quit.

因为指数级函数真的很致命，好，问题是。

麻省理工公开课 - 计算机科学及编程导论课程节选

Again, misleading-- fail to understand it because we don't understand the nature of exponential change.

再一次，误导…,没有理解指数函数，因为我们不理解,指数变化的本质。

哈佛公开课 - 幸福课课程节选

For most people, it seems extraordinary because people don' understand the nature of exponential function and therefore don't understand the nature of the power of one.

很多人会觉得不可思议,因为他们不懂指数函数的本质,也不懂“一“的力量。

哈佛公开课 - 幸福课课程节选

Because we underestimate the growth of exponential function.

因为我们低估了指数函数的增长。

哈佛公开课 - 幸福课课程节选

This is the nature of an exponential function.

这是指数函数的本质。

哈佛公开课 - 幸福课课程节选