常微分方程的级数解法探源

On the Origin of the Method of Series for Ordinary Differential Equation Solution

级数法是求解常微分方程最有效的方法之一.牛顿是第一位真正开始求解微分方程的数学家,级数法是其采用的第一种求解方法.在研读牛顿的微积分论文《流数法与无穷级数》基础上,探讨级数法形成的根源,揭示其思想方法对今日微分方程课程教与学的启迪作用以及对创立和发展微分方程学科的重要理论意义.

Method of series is one of the most effective approaches in seeking a solution of ordinary differential equations. In this aspect Newton was the first mathematician and method of series is the first means he used. On studying in his outstanding literature on method of series and theory of fluxions, the origin of the method of series is discussed. The enlightenment effect of method of series in teaching and studying in differential equations and its important role for founding and developing of the subject of differential equation are displayed.