第一型曲线积分与曲面积分的一些问题

第1型曲线积分与曲面积分的1些问题

摘 要

本文归纳研究了第1型曲线积分与曲面积分的物理背景，定义，性质及计算方法，并在此基础上给出了它们在特殊坐标变换下的计算公式及证明。并且利用这个公式，推导出了当第1型曲线积分或曲面积分的被积函数为奇函数或偶函数，积分曲线或曲面是对称的时的几个重要的推论及证明。

关键字：第1型曲线积分与曲面积分；坐标变换；奇偶性；对称性。

Some questions about curve integral and surface integral of the first kind

Abstract

In this article we induce and study the physical background ,definition, quality ,and calculating method of the curve and surface integral of the first kind ,and at the base of these , calculate formula and providence was proposed in the special coordinate transformation. Using this formula ,we get several important inference and prove that when the curve and surface integral of the first kind’s integrand is odd function or even function and the integral curve or surface is symmetry.

Key word: Curve integral and surface integral of the first kind; coordinate transformation; odevity; symmetry