中文摘要：

在处理多元微积分的很多问题时,我们可以将该函数局部地看作一次式,也就是局部看作它的微分式,而用线性代数的观点来处理,会给理解和记忆带来很大便利.这样给出的证明简单明了,不失严谨,它本质上是微积分“以直代曲”的表现.本文给出几个常见的困扰教学问题的简单证明.

英文摘要：

To simplify the problems in multi-variable calculus, this paper views a function to be linear lo- cally and treats the problems as linear problems. This method is essentially the nature of calculus. This paper also uses this method to solve a few of intriguing problems.