ON INTERPOLATION AND APPROXIMATION BY RATIONAL FUNCTIONS WITH PREASSIGNED POLES

<正> 1. INTRODUCTION. It is the purpose of this paper to presentsome results,on the problem of interpolation and approximation toa functiou f(z),analytic on a closed limited point set E in thecomplex z-plane whose complement K is connected and regular inthe sense that Green's fumction for K exists,by rational functionsf_n(z) of respective degrees n,n=1,2,…of the form     

微分方程理论的发展及其重要分支

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