滁州学院学报
滁州學院學報
저주학원학보
Journal of Chuzhou University
2010年
2期
1~2
,共null页
偏导数 方向导数 梯度 切平面 全微分 几何背景
偏導數 方嚮導數 梯度 切平麵 全微分 幾何揹景
편도수 방향도수 제도 절평면 전미분 궤하배경
partial derivative; directional derivative; gradient; tangent plane; total differential; geometrical background
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.
從一元函數到多元函數,有本質的差彆,但也有一些聯繫,如何把高維問題轉化為低維問題是科學研究的有效方法之一.藉助一元函數變化率的概唸,通過對多元函數微分學中的偏導數、方嚮導數、梯度、切平麵、全微分等幾箇相關概唸的幾何揹景的研究,幫助學生理解掌握這些重要概唸.
종일원함수도다원함수,유본질적차별,단야유일사련계,여하파고유문제전화위저유문제시과학연구적유효방법지일.차조일원함수변화솔적개념,통과대다원함수미분학중적편도수、방향도수、제도、절평면、전미분등궤개상관개념적궤하배경적연구,방조학생리해장악저사중요개념.
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.
