摘要
目的探讨和分析拉格朗日(Joseph Louis Lagrange,1736—1813)重新定义一阶偏微分方程完全积分概念的原因和背景。方法历史分析和文献考证。结果拉格朗日从欧拉的完全积分定义出发,在用常数变易法探讨一阶偏微分方程积分的过程中受到启发,萌生了关于积分"完全性"的新思想。随后,他把这种新思想运用于常微分方程,成功解释了奇解现象,受此驱动,提出了一阶偏微分方程完全积分的新定义。结论拉格朗日的完全积分新定义是他追求方程一般性解法的体现和产物。
Aim To explore the reasons why Lagrange redefined the concept of the complete integral of a first-order partial differential equation.Methods Historic analysis and literature review.Results Lagrange hit upon the new idea to redefine the complete integral when he received the inspiration from his study on the first-order partial differential equation with the method of variation of constants.When he used this new idea to research the ordinary differential equation,he explained the singular integral successfully.Inspired by his method,Lagrange formally put forward his new concept of the complete integral.Conclusion Lagrange＇s new definition showed his spirits of pursuing the general solution of the partial differential equation.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第4期675-679,共5页
Journal of Northwest University（Natural Science Edition）
基金
全国教育科学"十五"规划重点课题国家一般课题资助项目(BHA050023)
