多元函数微分学中几个相关概念的几何背景

Geometrical Background of Some Relevant Concepts of Differential Calculus for Function of Several Variables

从一元函数到多元函数,有本质的差别,但也有一些联系,如何把高维问题转化为低维问题是科学研究的有效方法之一.借助一元函数变化率的概念,通过对多元函数微分学中的偏导数、方向导数、梯度、切平面、全微分等几个相关概念的几何背景的研究,帮助学生理解掌握这些重要概念.

It is an effective method to make a scientific research by transforming higher dimensional problems into lower dimensional ones.There are essential differences but some relationships between function of one variable and function of several variables.In light of the transformation moduli of function of one variable,the geometrical background of some concepts of partial derivative,directional derivative,gradient,tangent plane and total differential of differential calculus for function of several variables is discussed in this paper,which will be helpful for the students to understand differential calculus for function of several variables.