1 微分方程的来源与作用.科学的物理学,从伽利略对於自由落体的试验开始.但那时因为还没有微积分,所以由试验结果所得到的规律,还不能简单明白的表达出来.自从牛顿和莱布尼兹发明了微积分以後,自由落体在真空中所遵从的定律.就可以用一个很简单的微分方程表出,即(1) (d~2y)/(dt~2)=-g其中g是地心吸力常数,t代表时间,y代表该落体在t时高出地面的距离(从下往上量).积分(1)式两次,即得 1 The origin and role of differential equations. Scientific physics began with Galileo’s experiment of free fall. But at that time, because there was no calculus, the laws obtained from the experimental results could not be expressed simply. After Newton and Leibniz invented calculus, the law of freefall falling in vacuum can be expressed by a very simple differential equation, ie (1) (d~2y)/(dt~2)= -g where g is the geocentric suction constant, t represents time, and y represents the distance of the falling body from the ground at t (from bottom to top). Integral (1) is twice, ie