多元函数几个概念的关系的研究

多元函数的连续性、可微性、偏导数、方向导数等概念比较抽象,关系复杂,是教学中的四大难点,难以理解,难以掌握。为了理清这些概念的内涵与关系,通过具体实例,充分利用有关概念与定理,详细讨论每一个概念的条件与结论之间的因果关系,以及这些基本概念之间的内在联系,给高等数学的教学降低难度,让初学者容易接受这些知识。

The Study on the Connection of Several Concepts of Multivariate Function

The concept of multiple functions, such as continuity, differentiable, partial derivative, directional derivative, is abstract and complex. They are the four special difficulties in teaching. In order to comprehend the connotation and concept of them, through concrete examples, we make full use of the concepts and theorems, and discuss in detail the causal connection between the conditions and conclusions of each concept, and the inner link between these basic concepts, which reduce the difficulty of teaching higher mathematics, which help beginners accept these knowledge easily.