微积分中积分的统一与运算

The Unity and Computation of Integral in Calculus

数学分析中研究的多种积分,都是通过分割、求和、取极限的过程建立的,它们在形式上差别很大但是其数学本质是一致的.在给出这些积分统一抽象表示的基础上分析了积分运算中的换元法与外微分之间的关系.最后讨论了使用微元法建立各种积分时微元选取的条件,并通过实例说明统一表示的方便.

All integrals in mathematical analysis are established by segmentation,summation,and taking limit.Although they vary widely in form,they have the same mathematical essence.This paper gives a unity representation of these integrals.Based on this representation,we analyze the relationship between substitution method and exterior differential.Finally we give the conditions of selecting approximation in using micro-element method and an example to illustrate the convenience of the uniform representation.