第三代的微积分

微积分已经有三百多年的历史了，由牛顿和莱布尼兹创建的微积分，是第一代微积分。第一代微积分，是说不清楚的微积分。以严格的极限理论为基础的微积分为第二代微积分。第二代微积分由于概念和推理繁琐迂回，成为了当今高等数学教学的难点。通过对导数和积分定义的研究，提出了甲函数和乙函数的概念，以此为基础建立起来的初等化微积分系统通俗易懂而又具有严格的理论基础，我们称之为第三代微积分。由于第三代微积分是以初等数学为基础，从而可大大降低教学的难度，另一方面又可利用目前在数学机械化取得的成果，实现微积分的机械化。

The Third Generation of Calculus

Calculus has been developing for almost three hundreds years.It was first introduced by Newton and Leibniz.Without the basis of rigorous theory,it was ambiguous,which is called the first generation of calculus.Later,it was established on the concept of limit in a rigorous and abstract way,called the second generation of calculus.However,it is difficult to understand for most beginners.In this paper,we introduce two concepts of function A and function B,on which a new calculus is built in a rigorous and simp...