摘要
针对现有数学分析教材对二元函数一致连续性介绍的不足,详细讨论二元函数一致连续性的四则运算和复合函数的一致连续的条件.其次,用实例的形式对二元函数一致连续性和函数有界、偏导数有界、方向导数有界以及可微之间的关系做了详细的注解.最后,给出了二元函数一致连续区域可加性的条件,并用实例的形式对二元函数和一元函数的一致连续性做了比较.
According to the scarcity of uniform continuity with binary function in the text books,this paper will study the fundamental operationson the uniformcontinuitywith binary functions and the conditionsof uniformcontinuity for composite function in detail.Secondly,we will analyze with examples the relationships between uniform continuity and boundness of function,between uniform continuity and boundness of partial derivative,between uniform continuity and boundnessof direction derivative,between uniformcontinuity and total differential forbinary functions.Lastly,we will study the conditions on regional additivity for uniform continuuity and also with an example,remark the difference on this result between unary function and binary function.
出处
《湘南学院学报》
2013年第5期1-6,共6页
Journal of Xiangnan University
基金
数学天元基金项目(NO.11226143)
湖南省自然科学基金项目(13JJ4111)
湖南省教育厅科研项目(10C0524
11B029)
湖南第一师范学院科学研究项目(XYS10N11
XYS11N03)
关键词
二元函数
一致连续
四则运算
偏导数有界
区域可加性
binary function
uniform continuity
fourfundamental operation
boundnessof partial derivative
regional additivity
