File:NLC416-08jh009087-25865 微分方程初步.pdf

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微分方程初步   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
〔美〕柯痕(Abraham Cohen)著
image of artwork listed in title parameter on this page
Title
微分方程初步
Publisher
世界書局
Description

目錄
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。常微分方程與偏微分方程。級與次。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 一級一次之微分方程differential equations of the firat order and first degree
5 正合微分方程。積分因子。exaot differential equation integrating factor
6 解題通則general plan of solution
7 方程為正合之條件conlition that equation be exact
8 正合微分方程 exact differential equations
9 分離變數及可離變數variables separated or separable
10 齊次方程homogeneous equations
11 方程中m及n為線性式而非齊次者equations in which m and n are linear but not homogeneous
12 方程式為yf1(xy)+xf2(xy)dy=o.equntions of the form yf1(xy)dz+xf2(xy)dy=o.
13 一級線式方程 linear equations of the order
14 方程之可化為線性式者 equations redueible to linear equations
15 方程式之為xrys(mydx+nxdy)+xρyσ(μydx+vxdy)=o
16 積分因子之可由視察而得者inetgrating factora by inspection
17 積分因子之可由他法求得者other forma for which integrating factors can be found
18 變數之變換transformation of variable
19 本章提要summary
第三章
應用applications
20 曲線之微分方程differential equation of a family of curves
21 幾何問題包含微分方程這geometrieal problems involving the solution of differential equations
22 正交曲線orthogonal trajectories
23 物理問題之引起微分方程者phyaical problema giving rise to differential equations
第四章
一級高次之微分方程differential equations of the first order and higher degree than the first
24 方程之可解為p之等式者equations solvable for p
25 方程之可解為y之等式者equations solvable for y
26 方程之可解為z之等式者equations solvable for z
27 克雷勞方程clairaut,s equation
28 本章提要summary
第五章
異解singular solutions
29 包線envelopea
30 異解singular solutions
31 判別式discrimjnant
32 由微分方程直接求得之異解singular solutions obtained directly from the differential equations
33 額外軌跡extraneous locl
34 本章提要summary
第六章
全微分方程total differential equations
35 全微分方程total differential equations
36 解法method of solution
37 齊次方程homogeneous equations
38 含有三變數以上之方程equations involving more than three variables
39 不能滿足積分可求條件性之方程equations which do not satisfy the conditiona for integrability
40 幾何的解釋geometrical interpretation
41 本章提要summary
第七章
常係數線性微分方程linear differential equations with constants coeffieients
42 線性微分方程通式general linear differential equations
43 常係數線性微分方程式，補充函數linear differential equations with constant coefficients,complementary function
44 輔助方程之根有重複者roots of auxitiary equation repeated
45 輔助方程之根為複數者roots of auxitiary equation complex
46 (d-α)符號之性質properties of the symbolio operator(d-α)
47 特別積分partieular integral
48 求特別積分之又一法another method of finding the partioular integral
49 參數變動法variation of parametera
50 待定係數法method of undetermind coeffieients
51 歌西線性方程式cauchy,s linear equation
52 本章提要summary
第八章
二級線性微分方程linear differential equations of the second order
53 依變數變換法change of dependent variable
54 自變數變換法change of inddependent variable
55 本章提要summary
第九章
解一級以上高級方程之雜法miscellansous methods for solving equations of higher order than the first
56 解題通則general plan of solution
57 缺依變數之方程dependent variable abaent
58 缺自變數之方程independent variable absent
59 線性方程而其特別積分有為已知者linear equations with partioular integral known
60 正合方程積分因子exact equation integrating factor
61 變數變換法 transformation of variables
62 本章提要summary
第十章
聯立方程組syatems of simuitaneous equations
63 解題通則general plan of solution
64 常係數線性方程組systems of linear equations with constant coeffici nta
65 一級方程組systems of equations of the fist order
66 幾何的解釋geometrical interpretation
67 全微分方程組systems of total differential equations
68 高級微分方程常可化為一級方程組differential equational of high crder than the first rsducible to systems of equationas of the first order
69 本章提要summary
第十一章
以級數求積分法integration in series
70 存在定理the existence theorem
71 異解singular solutions
72 以級數求一級方程之積分integration.in seties,of an equation of the firat crder
73 里卡提方程riccati,a equation
74 以級數求高級方程之積分法integration,in series,of equations of highar order than the first
75 高思方程。超比級數gauss,s equation.hypergeometrie seires
第十二章
偏微分方程partial differential equation
76 根式之含任意常數者primitivea involving arbitrary constants
77 根式之含任意函數者primitives involving arbitrary funotions
78 偏微分方程之解案solution of a partial differential equation
第十三章
一級偏微分方程partial differential equations of he first order
79 一級線性偏微分方程。拉格〓諸法。linear partial differential equations of the first order.method of lagrange
80 常微分方程mdx+ndy=o之積分因子。integrating factors of the ordinary differential equation mdx+mdy=o
81 一級非線性偏微分方程、全解、通解、異解nonlinea partial differential equations of first order.complete general singlar solutions
82 拉格〓諸及嘉華法method of lagrange and charpit
83 特別解法special methods
84 本章提要summary
第十四章
高級偏微分方程partial differential equations of hihger o rder than the first
85 第二微分為線性的二級偏微分方程者。蒙奇法fartial differential equations of the second order,linear in the second derivatives.monge,s method
86 特別解法special methods
87 線性偏微分方程通式general lin ar partial differential equations
88 常係數齊級一次方程homogeneous linear equations with conatant coeffieients
89 輔助方程之根有重複者roots of auxitiary equation repeated
90 輔助方程之根為複數者roots of auxitiary equation complex
91 特別積分partieular integral
92 常係數非齊級線性方程non-homogeneous linear equations with constant coefficients
93 方程之可化為常係數線性方程者equations reducible to linear equations with constant coefficients
94 本章提要summary
附錄notes
ⅰ. 包含兩個相同變數之兩函數科有關係存在之條件condition that a relation exist between two funetions of two variables
ⅱ. 本書提要general summary
答案answers to examples
索引index
增錄
目錄
ⅰ. 求特別積分另法
ⅱ. 弗洛白尼司法
ⅲ 含三個（或三個以上）自變數之偏微分方程之解法
ⅳ 解rr+ss+tt+u(rt-s2)=v之蒙奇法
ⅴ 福里哀之半段級數

Language Chinese
Publication date 民國21[1932]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
微分方程
中圖分類
InfoField
O175
載體形態
InfoField
272,31頁

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