摘 要:本文主要是通过分析实例来对多元微分学进行研究，对多元微分学中的二元函数的可微可导及连续性和他们之间的因果关系进行研究，在推广到多元函数，进而总结多元函数的可微可导及连续性之间的关系.文中我们有对二元函数的实例进行详细的分析和证明，并且通过建立他们之间的关系图来促进我们更加有效的理解和掌握多元函数微分学知识，加深我们的认识.相对一元的微分学来说，多元微分学和它很相近，但是从一元拓展到多元中间有很多本质的不同，但是从二元到多元微分学就只有一些技巧上面的差异，而没有本质的差别.深入学习多元微分学我们要记住两点，不仅要注意把握他们的相同之处，也要注意区分他们的不同之处.40065
毕业论文关键词：二元函数;可微;可导;连续
Function Differentiability Can be Interconnected Between Guide and Continuity
Abstract: Through the analysis of examples,the article is mainly to study of multivariate differential calculus and to study binary function's differentiable, can guide and continuity and the causal relationship between them belong to multivariate differential calculus ,then extended to multivariate function , and then summarizes the relationship of the function of many variables between differentiable ,can guide and continuity. In this paper, we have to a detailed analysis of the instance and certification of the binary function,and through the establishment of the relationship between their figure to promote us to understad and grasp the knowledge of multivariate function differential calculus more efficient and deepened our understanding. Relative to signal variable differential calculus, multivariate differential calculus is very close to it. but extend unitary to multiple , there is a lot of differences in nature.While there is no essential difference between binary and multivariate differential calculus,what difference exitence are only in some skills . In order to learn more multivariate differential calculus we should remember two points, not only should pay attention to grasp their similarities, also need to pay attention to distinguish the difference between them.
Key Words：Bivar function；Differentiable；Can guide；Continuity
目 录
摘 要 1
引言 3
1.一元函数的性质(可微性、可导性、连续性) 4
1.1性质之间的关系 4
1.2.函数的可导性与连续性 5
1.2.1 狄利克雷(Dirichlet)函数 5
1.2.2仅仅在一个点处连续，但不可导的函数 5
1.2.3只在一点可导且只在一点连续的函数 6
1.2.4 存在处处连续处处不可导的函数. 6
1.2.5 不连续但是处处可导的函数. 7
2．二元函数的可微、可导以及连续性 7
2.1偏导函数可微但并不一定连续. 9
2.2函数在一点连续且偏导存在不是函数可微的充分条件. 10
2.3偏导存在和函数连续并不存在必然联系 10
3．对于m元函数的一般情形 11
4.结束语 15
参考文献 16
致 谢 17
函数可微、可导及连续性之间的相互联系引言
微积分在高等数学中占有很重要的地位，是我们认识客观世界的重要途径之一，是我们学习其他自然科学和深入研究数学的基础.现如今微积分不仅仅是数学的一个部分，在物理、化学、生物、建筑学、计算机领域都是很重要的组成部分，而且现在微积分所反映的思想，在经济学、社会学以及我们的日常生活中工作中对我们认识和解决问题提供了一种思路. 函数可微可导及连续性之间的相互联系:http://www.751com.cn/shuxue/lunwen_38296.html