矩阵方法分解有理函数  

A Matrix Method for Decomposition of Rational Functions

作　　者：郑宝东[1] 张春蕊[2] ZHENG Bao-dong;ZHANG Chun-rui(Department of Mathematics,Harbin Institute of Technology,Harbin 150001;Department of Mathematics,Northeast Forestry University,Harbin 150040)

机构地区：[1]哈尔滨工业大学数学学院,哈尔滨150001 [2]东北林业大学理学院,哈尔滨150040

出　　处：《大学数学》2019年第6期85-91,共7页College Mathematics

基　　金：黑龙江省教育厅2019年教学改革项目(适合高校大班数学课的混合式教学模式探究)

摘　　要：有理函数积分的难点在于求出有理函数分解为部分分式之和的系数.目标是通过一个可逆矩阵求出分解系数.这种方法克服了待定系数法、极限法以及奥氏(M.V.Ostrogradsik)方法等通常方法的不足,给出的分解公式简洁明了,有利于理论分析,有利于教学实践,有利于借助计算机解决实际问题.The difficulty in integral of a rational function is to find the coefficients in decomposition of rational functions into the sum of partial fractions.Our goal is to find the decomposition coefficients using an invertible matrix.The method overcomes the deficiency of the usual methods,such as the method of undetermined coefficients,the method of limits,the method of Ostrogradsik,and so on.The decomposition formula is simple and clear.It is conducive to theoretical analysis,teaching practice and solving practical problems with the help of computers.

关 键 词：矩阵 有理函数 部分分式 分解 

分 类 号：O172.2[理学—数学]