符号函数在一些分片函数及其导数计算中的解析表示  

Analytic representations of symbol functions in some piecewise functions and calculations for their derivatives

作　　者：刘婷婷[1] 王贵君[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2013年第3期17-21,38,共6页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60974144)

摘　　要：利用3种符号函数研究分片函数及其导数的解析表示.首先,利用实例和第1种符号函数的特性讨论一元分段函数及其导函数的表示,并给出了连续可导的分段函数及其导数的一般解析表达式.其次,利用实例及第2种符号函数的特性研究多元分片函数的偏导数及其简化表示.最后,借助第3种符号函数探究单增跳跃函数广义导数的解析表示.Analytic representations of piecewise functions and their derivatives are discussed by using three kinds of symbol functions.Firstly,one variable piecewise functions and the representation of their derived functions are discussed by using examples and the characteristics of the first symbol function,and the general analytic expressions of continuous derivable piecewise functions and their derivatives are given.Secondly,the calculation for the partial derivative of multivariate piecewise functions and their simplified representations are studied in the light of specific examples and the characteristics of the second symbol function.Finally,the analytic representations of generalized derivates of increasing jump functions are explored by using the third symbol function.

关 键 词：符号函数 分片函数 单增跳跃函数 导数 解析表示 

分 类 号：O172.1[理学—数学]