If you knew only the third derivative of the function, you can have something quadratic in t without changing the outcome.

如果方程里有三阶导数,你就可以引入一个二次项,但是结果却不会变

耶鲁公开课 - 基础物理课程节选

What's a function, what's a derivative, what's a second derivative, how to take derivatives of elementary functions, how to do elementary integrals.

什么是函数,什么是导数,什么是二阶导数,如何对初等函数求导,如何进行初等积分

耶鲁公开课 - 基础物理课程节选

One way to think about this intuitively if the derivative is very large the function is changing quickly, and therefore we want to take small steps.

关于这个方法很直观的一点想法是,如果导数非常大,函数也就变化的非常快，因此我们想一小步一小步的来。

麻省理工公开课 - 计算机科学及编程导论课程节选