常微分方程组求解的案例式教学探索  

Case Teaching Investigation of Solving Ordinary Differential Equations

作　　者：李颖[1] 倪谷炎[1] 周敏[1] 

机构地区：[1]国防科学技术大学理学院数学与系统科学系,湖南长沙410073

出　　处：《大学数学》2015年第1期97-101,共5页College Mathematics

基　　金：公共基础数学系列研究生一流课程体系建设项目

摘　　要：常微分方程在高等数学中占有很重要的地位,在该部分内容的教学过程中引入适当的教学案例,旨在激发学生学习常微分方程的热情和提高学生解决实际问题的能力.本文以传输线理论中的微分方程—电报方程求解为教学案例,在给出案例的研究背景和数学描述之后,求解电报方程获得了集总源激励下的传输线终端响应,并结合具体算例分析其物理意义.Ordinary differential equations play an extremely important role in advanced mathematics.The purpose of the introduction of appropriate teaching cases during the teaching process of advanced mathematic is to stimulate students’ enthusiasm to study ordinary differential equations and improve students’ ability to solve pratical problems.The solution of telegrapher’s equations in transmission line theory was taken for case study as a form of differential equations.After the research background and mathematical description of case are introduced,the terminal responses of the transmission line under lumped sources excitation is acquired by solving the telegrapher’s equations Moreover,their physical significance was analyzed with the adoption of computational examples.

关 键 词：常微分方程 案例式教学 传输线响应 

分 类 号：O13[理学—数学] G642.1[理学—基础数学]