重节点牛顿均差插值在微积分学中的应用  

Application of Newton Interpolation with Multiple Nodes in Calculus

作　　者：郑华盛[1] 明万元[1] 袁达明 ZHENG Hua-sheng;MING Wan-yuan;YUAN Da-ming(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China;School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063 [2]江西师范大学数学与统计学院,南昌330022

出　　处：《南昌航空大学学报（自然科学版）》2023年第4期52-55,65,共5页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(118610391);2020年江西省研究生优质课程数值分析建设项目(2020-36);南昌航空大学教改课题(JY21056,JY22071,SZ2243)。

摘　　要：通过积分上限函数转化问题,基于重节点均差表及牛顿均差插值多项式确定辅助函数,构造和编制了一类含中介值的微积分等式证明题,得到了几个命题。Through the original problem of transforming the integral upper limit function,the auxiliary function has been determined based on the divided difference table with multiple nodes and the Newton interpolation polynomial.A class of equalities in calculus with mean value have been constructed and compiled,and several propositions have been obtained.

关 键 词：重节点 均差 牛顿插值多项式 微积分 积分上限函数 

分 类 号：O241.3[理学—计算数学]