## 曲线积分与积分路径无关性的应用

关键词:曲线积分;全微分;积分
Application Independence of
Curvilinearintegral and the Integration Path
Abstract: This paper introduces the four equivalent conditions plane curve path integral equivalent conditions unrelated to the four points of space curves and path independence, combined with examples of their application: calculated curve points, find the original function, seeking differential equations, find the equations of unknown function, especially in the case of unknown function required to solve a series of use associated with the path integral curves of differential equations seeking independence unknown function problems.
Key word: Curve Points; Fully Differential; Points

1.平面曲线积分与路径无关性的定理及证明    3
1.1利用平面曲线积分与路径无关性求原函数    6
1.2利用平面曲线积分与路径无关性求微分方程的解    7
1.3利用平面曲线积分与路径无关性计算曲线积分的值    9
1.4利用平面曲线积分与路径无关性求未知函数    11
2.空间曲线积分与路径的无关性定理及证明    12
2.1利用空间曲线积分与路径无关性求原函数    15 源自%六[维%论*文\$网.加7位QQ3249^114 www.lwfree.cn
2.2利用空间曲线积分与路径无关性计算曲线积分    16

1.平面曲线积分与路径无关性的定理及证明

首先介绍单连通区域的概念.
若对于平面区域 上任一封闭曲线,皆可不经过 以外的点而连续收缩于属于 的某一点,则称此平面区域为单连通区域,否则称为复连通区域. 曲线积分与积分路径无关性的应用:http://www.lwfree.cn/shuxue/20170523/7665.html
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