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File:NLC416-13jh008473-61765 微分方程式.pdf

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微分方程式   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
D. A. Murray著
image of artwork listed in title parameter on this page
Title
微分方程式
Publisher
龍門聯合書局[發行者]
Description

目錄
包含二變數之方程式
第一章 定義 微分方程式之構成
1 常微分方程式與偏微分方程式 階與次
2 解與積分常數
3 微分方程式之推求
4 通解 特解 奇解
5 一階一次微分方程式之幾何意義
6 一次或一階以上微分方程式之幾何意義
第一章 習題
第二章 一階及一次方程式
7 引言
8
9 x與y之相齊方程式
10 x與y之一次非齊方程式
11 恰當微分方程式
12 一階方程式為恰當方程式之條件
13 求恰當微分方程式之解的規則
14 積分因子
15 積分因子為數無窮
16 用視察法求積分因子
17 求積分因子之規則 規則i與ii
18 規則iii與iv
19 規則v
20 線性方程式
21 可化為線性型之方程式
第二章 習題
第三章 一階而非一次之方程式
22 方程式之能分解為一次分方程式者
23 方程式之不能分解為分方程式者
24 方程式之可解得y者
25 方程式之可解得x者
26 方程式之不含x或不含y者
27 x與y相齊之方程式
28 x與y之一次方程式 克來洛方程式
29 概要
第三章 習題
第四章 奇解
30 參考代數學及幾何學
31 判別式
32 包絡
33 奇解
34 克來洛方程式
35 p及c判別式關係中可能出現之關係（非解）
36 自切點軌跡之方程式
37 結點軌跡之方程式
38 歧點軌跡之方程式
39 概要
第四章 習題
第五章 在幾何學力學及物理學方面之應用
40 引言
41 幾何問題
42 幾何學之已知件
43 例題
44 有關軌線之問題
45 軌線 直角坐標
46 正交軌線 極坐標
47 例題
48 力學及物理學問題
第五章 習題
第六章 常係數線性方程式
49 線性方程式定義 補函數 特積分 全積分
50 係數為常數而右端為零之線性方程式
51 輔助方程式具有等根之例
52 輔助方程式具有虛根之例
53 記號d
54 關於d之定理
55 輔助方程式具有重複根時另一求解之方法
56 係數為常數與右端為x函數之線性方程式
57 記號函數〓
58 特積分求法
59 在某種情況中求特積分之簡法
60 積分之與右端中〓型之項相當者
61 積分之與右端中〓型之項相當者
62 積分之與右端中〓或〓型之項相當者
63 積分之與右端中〓型之項相當者
64 積分之與右端中〓型之項相當者
第六章 習題
第七章 變係數線性方程式
65 齊性線性方程式 第一解法
66 第二解法：（a)求補函數
67 第二解法：（b)求特積分
68 記號函數f(o)〓
69 特積分求法
70 積分之與右端中〓型之項相當者
71 可化為齊性線性型之方程式
第七章 習題
第八章 恰當微分方程式及特型方程式 用級數解法
72 引言
73 恰當微分方程式定義
74 恰當微分方程式之判別準則
75 恰當方程式之積分法 第一積分
76
77
78 方程式之不直接含有y者
79 方程式之不直接含有x者
80 方程式之其中y僅出現於相差兩階之二導數中者
81 方程式之其中y僅出現於相差一階之二導數中者
82 線性方程式之用級數解法
83 勒襄特，貝塞爾，里卡提及超越幾何級數之方程式
第八章 習題
第九章 二階方程式
84 引言
85 以一已知積分表達全角
86 各積分間之關係
87 用視察法求解
88 用運算因子求解
89 用二個第一積分求解
90 改變因變數使方程式變換
91 移去第一階導數
92 改變自變數使方程式變換
93 二階方程式解法一覽
第九章 習題
第十章 幾何學及物理學中之應用
94 引言
95 幾何學之問題
96 力學及物理學之問題
第十章 習題
包含二個以上變數之方程式
第十一章 具有二個以上變數之常微分方程式
97 引言
98 聯立線性微分方程式
99 聯立一階方程式
100 聯立一階方程式積分之通式
101 包含三變數之聯立一階一次微分方程式之幾何意義
102 可積分之單微分方程式 可積分性之條件
103 可積分單微分方程式解法
104 可積分單微分方程式之幾何意義
105
106 不可積分之單微分方程式
第十一章 習題
第十二章 偏微分方程式
107 定義
108 由消去常數推求偏微分方程式
109 由消去泛函數推求偏微分方程式
一階偏微分方程式
110 非線性方程式之積分：全積分與特積分
111 奇積分
112 通積分
113 線性方程式之積分
114 相當於線性方程式之方程式
115 拉格郎奇線性方程式解法
116 拉格郎奇解法之核驗
117 含有二個以上自變數之線性方程式
118 線性偏微分方程式之幾何意義
119
120
121
122
123 一般解法
二階及高階偏微分方程式
124 二階偏微分方程式
125 易解之例題
126
127 高於一階之一般線性偏微分方程式
128 常係數之齊性方程式：補函數
129 輔助方程式有重複根或虛根時之解法
130 特積分
131 常係數之非齊性方程式：補函數
132 特積分
133 方程式之變換
134
135 特例
136
第十二章 習題
各項附註
a 化方程式為聯立一階方程式系
b 存在定理
c 積分常數之個數
d 積分常數獨立性之判別準則
e 恰當微分方程式之判別準則
f 線性方程式積分之線性無關性之判別準則
g 線性方程式積分與關係數間之關係
h
i 近代微分方程式論 不變式
j 記號d
k 用級數解法
習題解答
人名索引
題目索引
英漢數學名詞對照表
後記
學習捷程
（羅馬數字指章數，阿拉伯數字指節數）

Language Chinese
Publication date 民國三十八年[1949]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
館藏信息
InfoField
MG/O175/1
主題
InfoField
微分方程
中圖分類
InfoField
O175
載體形態
InfoField
240頁

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