一阶常微分方程的知识图谱  

Knowledge Graph of First Order Ordinary Differential Equations

作　　者：黎平 杨晓珍[1] LI Ping;YANG Xiaozhen(Kaili University,Kaili,Guizhou,556011,China)

机构地区：[1]凯里学院,贵州凯里556011

出　　处：《凯里学院学报》2024年第3期1-9,共9页Journal of Kaili University

基　　金：2023年凯里学院校级规划课题学生课题。

摘　　要：一阶常微分方程的方程类型较多,解法不一.在学习的过程中会因为方程类型的判断不准确,导致学习困难.本文通过构造一阶常微分方程的知识图谱,将繁杂的知识进行关联与梳理,呈现常见一阶常微分方程的方程类型和解法之间的相互关系,并以实例进行说明.构建微分方程的知识图谱可以对微分方程中的概念、方法和技巧等进行全面和系统地整合,呈现出方程之间的内在联系和逻辑关系,可以培养学生的逻辑思维能力,帮助学生更加深入和全面地学习微分方程的知识,提高学习效果.There are many types of first-order ordinary differential equations with different solutions.In the process of learning,it may be very difficult to learn because of inaccurate judgment of equation types.By constructing knowledge atlas of first-order ordinary differential equations,this paper relates and sorts out complex knowledge,presents the relationship between equation types and solutions of common first-order ordinary differential equations,and illustrates it with examples.Knowledge atlas of differential equations can be constructed to comprehensively and systematically integrate concepts,methods and techniques in differential equations.It not only presents the internal connection and logical relationship between equations,but also cultivates students logical thinking ability.What s more,it helps students to have a more comprehensive understanding and learning of differential equations,which is conducive to improve students learning effect.

关 键 词：知识图谱 常微分方程 常数变易法 积分因子 

分 类 号：O143[理学—数学]