如何不用复数讲解常系数线性微分方程  

How to Teach Linear Differential Equation with Constant Coefficients Not to Use Complex Number

作　　者：严质彬 包益欣 YAN Zhi-bin;BAO Yi-xin(School of Science,Harbin Institute of Technology Shenzhen,Shenzhen 518055, China)

机构地区：[1]哈尔滨工业大学(深圳)理学院,广东深圳518055

出　　处：《大学数学》2021年第1期68-71,共4页College Mathematics

基　　金：哈尔滨工业大学(深圳)教学研究项目(HITSZIP19008,HITSZUCP18014);国家自然科学基金项目(11801117)。

摘　　要：在高等数学课程中,复指数函数及其导数知识的严格讲解,通常要比微分方程知识的讲解晚很多.这使得微分方程的教学在逻辑上有些不足.用复值函数解的复系数线性组合推导出实值函数解,在教学实践中,学生经常感到迷惑.不以复数的任何知识作为前提,给出了常系数微分方程的一种自然的讲解方法.In the teaching of the course Advanced Mathematics,exponential function in complex variable is taught much later than differential equation.This causes that the teaching of differential equation,which needs the knowledge on exponential function in complex variable as prerequisite,lacks some satisfaction.Also,it is somewhat difficult for students to understand the skill of using solutions of complex-valued functions to deduce solutions of real-valued functions through linear combinations of complex coefficients.Without any knowledge on complex number as prerequisite,this paper gives a method to teach linear differential equation with constant coefficients naturally.

关 键 词：常系数线性微分方程 复数 欧拉公式 复指数函数 

分 类 号：O175.1[理学—基础数学]