15.1 导言:微积分预览

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  导言:微积分预览

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  While calculus has ancient roots, Sir Issac Newton (below left) and Gottfried Wilhelm Leibniz (below right)  developed  modern calculus a few hundred years ago to account for subtle paradoxes in their representations of the physical world. Calculus is Latin for "small pebble used for counting." It was originally based on the summation of counting infinitesimal differences. In other words, what happens when you add an infinite number of infinitely small numbers together? What happens when you divide  an infinitely small number ( $\begin{array}{r}dy\end{array}$ ) by another infinitely small number ( $\begin{array}{r}dx\end{array}$ )?  Calculus is basically the study of change. It includes a system of tools and a way of thinking about infinity that help make sense of these perceived paradoxes.
  ::虽然微积分有古老的根基,但Issac Newton爵士(左下方)和Gottfried Wilhelm Leibniz(右下方)在几百年前开发了现代微积分,以说明物理世界的表现形式中微妙的悖论。微积分是拉丁文的“用于计算的小卵石 ” 。 它最初基于计算无限微小差异的加和。 换句话说, 当你将无限小的数字加在一起时会发生什么呢? 当你将无限小的数字除以另一个无限小的数字( dx) 时会发生什么? 微积分基本上就是对变化的研究。 它包括一个工具体系和关于无限的思维方式, 帮助人们理解这些想象的悖论。