二重积分变量代换公式证明的探讨

The Study of the Variables Change Formula in Double Integrals

在一般教材中二重积分变量代换公式的证明通常采用几何的方法,也有部分数学分析教材给与了严格的分析证明,但证明不便直观的几何说明.本文对二重积分变量代换公式进行了一些探讨,给出了一个较简洁直观的分析证明方法.

The variables change formula in double integrals often is proved by the geometry method in many teaching materials. It often is difficult that the analytic proof of the formula are offered in other some teaching materials of differential and integral calculus. In this paper, we discuss and obtain an analytic intuitionistic proof method of the variables chang formula in double integrals and give a simple proof method.