关于常微分方程的发展及其应用的探悉研讨.doc

关于常微分方程的发展及其应用的探悉 姓 名： 佳木斯大学理学院数学系 2015年6月 摘 要 常微分方程是17世纪与微积分同时诞生的一门理论性极强且应用广泛的数学学科之一．常微分方程的形成与发展与力学、天文学、物理学及其他科学技术的发展密切相关，当前计算机的发展为常微分方程的应用及理论研究提供了非常有力的工具.常微分方程的理论和方法不仅广泛应用于自然科学，而且越来越多的应用于社会科学的各个领域 本篇文章从常微分方程的产生背景谈起，分四个时期介绍其发展过程．文章从常微分方程的产生背景、发展、应用等方面出发，系统地介绍常微分方程的发展史及其应用在数学发展中的重要意义． 关键词: 常微分方程；发展；应用 Abstract Ordinary differential equation is the 17th century with the birth of calculus and a strong theoretical and one of the widely applied mathematics. The formation and development of ordinary differential equations with mechanics, astronomy, physics and other closely related to the development of science and technology, The current development of the computer for the application of ordinary differential equation and the theoretical research provides a very powerful tool. The theory and methods of ordinary differential equation is not only widely used in natural science, And more and more applied in various fields of social science. This article from the background of ordinary differential equations, Point four periods to introduce its developing process. From the background of ordinary differential equation, development, application, etc, Systematically introduce the history of ordinary differential equation and its application in the important significance in the development of mathematics. Keywords: Ordinary differential equation; develop; application 目 录 摘 要．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． Abstract．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 绪论．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 常微分方程的发展史．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 2.1常微分方程的产生背景．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 2.2常微分方程的发展．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 2.2.1常微分方程经典阶段．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 2.2.2常微分方程适定性理论阶段．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 2.2.3常微分方程解析理论阶