一道考研预测题引起的思考

Thoughts Stemming from a Postgraduate Entrance Examination Problem

文中巧妙地经过思维转化,利用方向导数和坐标变换的思想将多元函数转化为一元函数,使得能够运用牛顿-莱布尼兹公式∫_a^bf'(x)dx=f(b)-f(a)来证明一个多元函数积分的问题.

This paper uses the ideas of directional derivatives and transformation to convert a multivariate function problem to a single variable function problem,which makes it valid to use the Newton- Leibniz formula to prove a proposition about a multivariate function.