File:NLC416-14jh000329-94120 微分幾何學.pdf

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微分幾何學   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
劉景芳編譯
image of artwork listed in title parameter on this page
Title
微分幾何學
Publisher
北平輔仁大學[發行者]
Description

目錄
第一卷 平面曲線
第一章 論包羅線
1 包羅線之尋求
2 直線之包羅線
3 圓之包羅線
習題一（1-6）
第二章 曲率
4 曲率半徑
習題二（1-5）
5 縮閉線與伸開線
6 擺線
7 垂鏈形曲線與等切曲線
8 橢圓之縮閉線
習題三（1-6）
9 自立方程式
習題四（1-3）
第三章 平曲線之接觸
10 接觸次數
11 解析法
12 吻合曲線
13 吻合曲線之性質
習題五（1-5）
習題六（第一卷總習題1-10）
第二卷 扭線
第一章 吻合平面
14 定義與方程式
15 停立吻合平面
16 停立切線
17 若干種特殊曲線
習題七（1-6）
第二章 曲面之包羅面
18 具有一參變數之一族曲面
19 具有二參變數之一族曲面
20 可展曲面
21 可展曲面之偏微分方程式
習題八（1-5）
22 一族扭線之包羅線
習題九（1-5）
第三章 扭線之曲率與扭率—縮閉線
23 球面指示線
24 曲率半徑
25 主法線.曲率中心
26 極直線.極曲面
習題十（1-3）
27 扭率
28 福來內氏（frenet）公式
29 x,y,z依s之展式
習題十一（1-5）
30 伸開線與縮閉線
31 螺旋線
32 貝特昂氏（j.bertrand）曲線
習題十二（1-7）
第四章 二扭線之接觸.曲線與曲面之接觸
33 二扭線之接觸
34 吻合曲線
35 一曲線與一曲面之接觸
36 吻合球
37 曲面之吻合直線
習題十三（1-8）
第五章 關於直線群之理論
38 直線曲面
習題十四（1-3）
39 二元直線群.焦曲面
習題十五（1）
40 曲面之法線所形成之二元直線群
習題十六（1-2）
41 三元直線群
習題十七（第二卷總習題1-16）
第三卷 曲面
第一章 在一定曲面上所畫出之曲線之曲率
42 基本公式.墨尼艾氏（meusnier）定理
43 關於（edu2+2fdudv+gdv2）與（ddu2+2d1dudv+d2dv2）兩個二次式之理論
44 尤拉氏（euler）定理，曲率指示線
45 主要曲率半徑
習題十八（1-15）
第二章 一曲面上最能惹人注目之各種曲線
46 正交軌道線
47 水平割線與坡線
習題十九（1-4）
48 地形圖志
習題二十（1）
49 漸近觸線
習題二十一（1-16）
50 直紋曲面之漸近觸線
習題二十二（1-2）
51 配偶曲線
習題二十三（1-5）
52 主曲率線
習題二十四（1-4）
53 一曲面之縮閉面
54 羅德里克氏（olinde rodrique）公式
55 若西慕斯遠氏（joachimsthal）定理
56 杜雨班氏（dupin）定理
習題二十五（1-3）
57 測地扭率
習題二十六（1）
58 應用以上所述之各種理論於若干類曲面
習題二十七（1-7）
第三章 二曲面上點與點間之對應法
59 球面表示法
60 能合曲面
61 《能合在一平面上》之各種曲面
習題二十八（1）
62 地平曲率.測地線
63 總曲率.高思氏（gauss）定理
習題二十九（1-4）
64 同形變換法
65 一平面在其他一平面上之同形表示法
66 同形平面地理圖
習題三十（1）
習題三十一（第三卷總習題1-7）
中西名詞對照表

Language Chinese
Publication date 民國三十年[1941]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
館藏信息
InfoField
MG/O186.1/1
主題
InfoField
微分幾何
中圖分類
InfoField
O186.1
載體形態
InfoField
316頁

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