浅谈常微分方程教学中解的存在唯一性定理  

On the Existence and Uniqueness Theorem of Solutions in the Teaching of Ordinary Differential Equations

作　　者：薛帅帅 邓海云 XUE Shuaishuai;DENG Haiyun(School of Statistics and Data Science,Nanjing Audit University,Nanjing,Jiangsu 211815)

机构地区：[1]南京审计大学统计与数据科学学院,江苏南京211815

出　　处：《科教导刊》2021年第27期115-117,共3页The Guide Of Science & Education

基　　金：2020年度国家自然科学基金项目“非线性薛定谔方程的可约化的KAM环面”(12001275)

摘　　要：物理、生物、化学以及工程技术中的大量问题,如果用数学语言加以精确描述,常常会出现微分方程,而解的存在唯一性定理又是解微分方程的前提和理论基础.本文主要探讨在常微分方程课程教学中证明解的存在唯一性定理的证明思路,目的是通过补充说明使证明更容易理解.解的存在唯一性定理的证明过程,提供了一个全面锻炼学生数学思维习惯与能力的契机,希望学生在学习过程中能更加深刻的理解其中所包含的想法,培养善于思考的学习习惯.If a large number of problems in physics,biology,chemistry and engineering technology are accurately described in mathematical language,differential equations often appear,and the existence and uniqueness theorem of solutions is the premise and theoretical basis for solving differential equations.This paper mainly discusses the proof idea of proving the existence and uniqueness theorem of solution in the teaching of ordinary differential equation,in order to make the proof easier to understand through supplementary explanation.The proof process of the existence and uniqueness theorem of solution provides an opportunity to comprehensively exercise students’mathematical thinking habits and abilities.It is hoped that students can more deeply understand the ideas contained in it and cultivate thinking learning habits in the learning process.

关 键 词：常微分方程 解 存在性 唯一性 

分 类 号：G424[文化科学—课程与教学论]