File:NLC416-08jh009389-22106 微積分學講義.pdf

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微積分學講義   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
[〔日〕根津千治著]
image of artwork listed in title parameter on this page
Title
微積分學講義
Publisher
商務印書館 (上海)
Description

目錄
上卷 微分學
前篇 本論
第一章 緒論
1 數之分類
2 變數及常數
3 連續變數及其區域
4 函數
5 函數之形式
6 函數之分類
7 逆函數
8 極限值
9 關於極限值之定理
10 無限大及無限小
11 無限小及無限小之位
12 函數之連續
13 連續函數與曲線
14 關於連續之定理
15 〓
第二章 微分法
1 微分，微分係數
2 微分係數與曲線
3 微分係數之函數
4 函數和之微分法
5 函數積之微分法
6 函數商之微分法
7 函數之函數之微分法
8 〓之微分係數
9 logx之微分係數
10 〓之微分係數
11 三角函數之微分係數
12 圓函數之微分係數
13 對數微分法
14 平均值之定理
第三章 累次微分法
1 累次導來函數
2 累次微分，累次微分係數
3 sinx及cosx之累次微分係數
4 〓,logx及〓之累次微分係數
5 函數之積之累次微分係數
第四章 偏微分法
1 含二個自變數之函數
2
3 偏微分係數，偏微分
4 全微分
5 累次偏微分法
6 函數之函數之偏微分法
7 同次函數
8 陰函數之導來函數
9 自變數之變換
10 自變數及函數之變換
第五章 級數
1 常數項之級數
2 正項之級數
3 正項級數之收斂之查定
4 正負項混雜之級數
5 冪級數
6 函數之展開
7 戴氏定理
8 馬氏定理
9 指數函數之展開
10 對數函數之展開
11 三角函數之展開
12 二項式之展開
13 用未定數之展開法
14 二個自變數之函數之展開
第六章 不定形
1 不定形之種類
2 0/0之不定形
3 ∞/∞之不定形
4 ∞－∞之不定形
5 〓,〓,〓之不定形
第七章 函數之極大極小
1 函數f（x）之極大極小
2
3 二個自變數函數之極大極小
後篇 平面曲線之應用
第八章 平面曲線總論
1 平面曲線之方程式
2 切線及法線
3 從曲線外引切線
4 切線，法線之長及其正射影
5 漸近線
6 代數曲線之漸近線漸近曲線
7 曲線之凹凸及彎曲點
8 極方程式之曲線
9 曲線之奇點
10 曲線奇點之查定
11 弧之微分
12 曲度
13 縮閉線及伸開線
14 包絡線
15 二個曲線之切觸
16 吻合曲線
第九章 平面曲線各論
1 曲線之追跡及其方法
2 直角坐標式之曲線追跡
3 極坐標式之曲線追跡
4 蔓葉形線（cissoidofdiocles）
5 葉形線（foliumofdescartes）
6 蚌殼形線（conchoidofnicomcdes）
7 雙紐形線（lemniscate）
8 心臟形線（cardioid）
9 蝸牛形線（limacon）
10 擺線（cycloid）
11 餘擺線（trochoid）
12 圓外擺線（epicycloid）及圓內擺線（hypo-cycloid）
13 亞奇默德氏之螺線（spiralofarchimedes）
14 對數螺線（logarithmicspiral）
15 垂絲線（catenary）
16 等切曲線（tractrix）
17 對數曲線（logarithmiccurve）
18 正弦曲線（linecurve）
下卷 積分學
前篇 本論
第一章 積分學之基礎
1 不定積分
2 積分常數
3 基本積分之公式
4 基本法則
5 變換積分法
6 部分積分法
7 定積分之意義
8 定積分與不定積分之關係
第二章 不定積分
1 有理整函數之積分
2 有理分數之積分
3 無理式〓之積分
4 無理式〓之積分
5 二項式〓之積分
6 含對數函數，逆三角函數之函數之積分
7 含指數函數之函數之積分
8 含三角函數之函數之積分
第三章 關於定積分之定理
1 定積分求值之法
2 平均值之定理
3 界限內不連續之函數之積分
4 界限無限大之積分
5 無限級數之積分
第四章 重積分
1 界限為常數之二重積分
2 界限為變數之二重積分
3 三重積分
後篇 曲線曲面等之應用
第五章 平面圖形
1 平面曲線包圍之面積
2 於極式坐標之面積
3 面積之例
4 面積之近似值
5 平面曲線之長
6 曲線之長之例
第六章 曲面
1 曲面之方程式
2 曲面之切平面及法線
3 曲面之指曲線及曲度
4 立體求體積之一般公式
5 單一積分之體積
6 二重積分之體積之例
7 三重積分之體積之例
8 曲面求面積之一般公式
9 單積分之曲面積
10 二重積分之曲面積之例
第七章 空間曲線
1 空間曲線之方程式
2 空間曲線之切線及法平面
3 空間曲線之吻合平面及主法線
4 空間曲線之弧之長
續篇 微分方程式
第八章 第一階微分方程式
1 定義
2 第一階一次微分方程式之解
3
4 同次微分方程式
5
6 全微分方程式
7 積分因數
8 奇異解
9 第一階二次微分方程式
10 缺少變數之高次微分方程式
11 苛盧里（clairaut）之微分方程式
第九章 第二階微分方程式
1 第二階微分方程式之解
2 微分方程式〓
3 微分方程式〓
4 微分方程式〓
5 微分方程式〓及〓
6 一般第二階微分方程式之種種例解
7 聯立第一階微分方程式
8 聯立第二階微分方程式
9 級數積分法
第十章 變分法
1 變分法之問題
2 變分
3 積分之極大極小
4 極小迴轉面
5 最速落着線

Language Chinese
Publication date 民國13[1924]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
微積分
中圖分類
InfoField
O172
拼音題名
InfoField
wei ji fen xue jiang yi
載體形態
InfoField
394頁

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