File:NLC416-13jh008429-58828 微積分學.pdf

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Summary[edit]

微積分學   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
孫光遠 孫叔平著
image of artwork listed in title parameter on this page
Title
微積分學
Publisher
商務印書館[發行者]
Description

目錄
第一章 函數及極限
1 常數，變數
2 函數及其圖表
3 初等函數
4 極限
5 函數之極限
6 關於極限值的定理
7 兩個重要極限值
〓
〓
8 函數的連續性
9 關於連續函數的基本定理
10 連續函數的特性
11 指數函數
12 對數函數
習題1
第二章 微分法
13 導數
14 導數的幾何意義
15 微分
16 簡單函數的導數
17 關於導數的基本定理
習題2
第三章 導數之性質及其應用
18 函數之增減與其導數之關係
19 rolle氏定理
20 中值定理
21 增函數，減函數
22 gauchy氏定理
23 函數之極大值與極小值
24 函數之近似值
習題3
第四章 逐次微分法
25 逐次導數
26 關於逐次導數的定理
27 求逐次導數之特別方法
28 反函數的逐次導數
29
30 逐次微分
31 無窮小
32 不定形
33 方程式論上之應用
34 物理學上之應用
習題4
第五章 平面曲線
35 切線，法線
36 弧微分
37 曲線之凹凸
38 切觸圓
39 曲率
40 縮閉線及伸開線
41 極座標
習題5
第六章 無窮級數
42 無窮級數
43 關於級數的基本定理
44 正項級數
45 交錯級數
46 絕對收斂級數
47 複數項級數
48 冪級數
49 冪級數之微分法
習題6
第七章 函數之展開
50 taylor氏定理
51 maclaurin氏定理
52 taylor氏級數及maclaurin氏級數
53 指數函數之展開
54 sin x 及cos x之展開
55 euler氏公式
56 雙曲線函數
57 log(1+x)之展開
58 對數之計算
59 二項級數
60 展開之特別方法
61 函數展開之應用
1°函數之近似值
2°不定形之極限值
3°極值之判定
習題7
第八章 不定積分
62 不定積分
63 積分的基本定理
64 代換積分法
65 部份積分法
66 幾個重要積分
67 雜例
習題8
第九章 定積分
68 定積分
69 積分值之存在
70 關於定積分的定理
71 定積分與不定積分的關係
72 由不定積分求定積分
1°基本公式
2°代換積分法
3°部份積分法
73 冪級數的積分法
74 無窮積分
75 收斂性的決定
76 瑕積分
77 平面形之面積
78 平面曲線之長
79 定積分之近似值（simpson氏之法則）
習題9
第十章 積分法
80 有理函數之積分
81 無理函數之積分
1°〓
2°〓
3°〓
82 超越函數之積分
1°〓
2°〓
習題10
第十一章 偏微分法
83 二變數的函數
84 偏導數
85 逐次偏導數
86 全微分
87 函數的函數之偏導數
88 taylor氏定理
89 函數f(x,y)之極值
90 隱函數之微分法
習題11
第十二章 幾何上的應用
91 切線，法線，特異點
92 漸近線
93 曲線之畫法
94 包線
95 空間曲線的切線及法平面
96 曲面的切平面與法線
97 切觸面
習題12
第十三章 重積分
98 重積分
99
100 重積分的求法
101 體積
102 變數之更換
103 旋轉體的體積
104 曲面的面積
105 旋轉面的面積
106 euler氏積分
107 重心
108 慣性能率
習題13
第十四章 微分方程式
109 定義
110 第一級微分方程式
111 常數係數第二級線性方程式
112 微分方程組
習題14
中英名詞對照表

Language Chinese
Publication date 民國二十九年[1940]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
館藏信息
InfoField
MG/O172/14
主題
InfoField
微積分
中圖分類
InfoField
O172
載體形態
InfoField
348頁

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current06:32, 11 June 2023Thumbnail for version as of 06:32, 11 June 2023891 × 1,210, 362 pages (6.25 MB)PencakeBot (talk | contribs)Upload 微積分學 (1/1) by 孫光遠，孫叔平著 (batch task; nlc:data_416,13jh008429,58828; 民國圖書.8; 微積分學)

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