微分方程初步.pdf电子版

目录简介

目录

第一章 微分方程及其解案differential equationa and their solutions

微分方程及其解案differential equations and their solutions

1 微分方程。常微分方程与偏微分方程。级与次。differential dqnation.ordmay and fartial order,degree

2 方程之解案 sotution of an equation

3 由根式求微分方程derivation of a differential equation from ita primitivo

4 通解，特解goneral,particular solution

第二章 一级一次之微分方程differential equations of the firat order and first degree

5 正合微分方程。积分因子。exaot differential equation integrating factor

6 解题通则general plan of solution

7 方程为正合之条件conlition that equation be exact

8 正合微分方程 exact differential equations

9 分离变量及可离变量variables separated or separable

10 齐次方程homogeneous equations

11 方程中m及n为线性式而非齐次者equations in which m and n are linear but not homogeneous

12 方程式为yf1(xy)+xf2(xy)dy=o.equntions of the form yf1(xy)dz+xf2(xy)dy=o.

13 一级线式方程 linear equations of the order

14 方程之可化为线性式者 equations redueible to linear equations

15 方程式之为xrys(mydx+nxdy)+xρyσ(μydx+vxdy)=o

16 积分因子之可由视察而得者inetgrating factora by inspection

17 积分因子之可由他法求得者other forma for which integrating factors can be found

18 变量之变换transformation of variable

19 本章提要summary

第三章

应用applications

20 曲线之微分方程differential equation of a family of curves

21 几何问题包含微分方程这geometrieal problems i......