File:NLC416-08jh009174-25568 代數學—順列組合及級數.pdf

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代數學—順列組合及級數   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
〔日〕佐藤充 〔日〕水田文平著
image of artwork listed in title parameter on this page
Title
代數學—順列組合及級數
Publisher
商務印書館[發行者]
Description

目錄
第一章 緒論
組合之定義
排列不同之物
順列之定義
第二章 順列
無遺漏無重複之順列之群
作順列群之方法
順列之數
計算順列之數
計算npr之公式
基本定理
從npr之關係求n之值
從npr之關係求r之值
npr間之關係式
npr之添數r=n之順列數
從n！求n之值
用階乘積表npr之值
記號0!之值
簡單之應用問題
有若干文字占一定之位置之順列
若干文字所占之位置有相互之關係求其順列之數
若干文字所占之位置有一定之範圍求其順列之數
有若干數字不拘定同時用幾數字之問題
用若干數字所作之數之和
重複順列
取不全異之物作順列求順列之數
豫定若干文字之次序作順列
排為二列或三列以上之方法
環狀順列
練習問題ⅰ
第三章 組合
表組合之數之記號
表組合之數之公式
以階乘表ncr之值
求證ncr=ncn-r
ncr之最大值
從ncr之添數r之值之關係求n或r之值
簡單之應用問題
選擇有限制之組合
選舉有區別之組合
從若干群分別選擇之組合
幾何學上之應用
從互異或不全互異之各物任意取若干物之情形
分配及分割
順列組合併用之問題
練習問題ⅱ
第四章 二項定理
二項因數之連乘積
公項
展開式中某文字之幾次冪之係數
與初項未項距離相等之項之係數亦相等
書展開式之簡便方法
最大係數
最大項
從展開式之若干項或其係數求指數或其他文字之值
係數之和
用二項定理求三項之諸乘冪之展開式
指數為分數或負數之二項定理
計算近似值
練習問題ⅲ
第五章 等差級數
級數之定義
等差級數
公項
等差中項
等差級數之和
推廣等差級數總和之公式之用
用聯立方程式之解法求等差級數未知之要素
應用問題
練習問題ⅰ
第六章 等比級數
等比級數之定義
公項
等比中項
相加平均數與相乘平均數
等比級數之和
推廣等比級數總和之公式之用
整除定理，剩餘定理
無限等比級數
循環小數
應用問題
練習問題ⅱ
第七章 調和級數
定義
調和中項
等差中項等比中項調和中項相互之關係
調和級數之和
練習問題ⅲ
第八章 他種級數之和
求級數1+2+3+4+……＋n之和
求級數1²+2²+3²+4²+……+n²之和
同類項之和之記號∑
求級數1³+2³+3³+4³+……+n³之和
求級數1.2+2.3+3.4+……至第n項之和
求級數1.2+2.5+3.8+……至第n項之和
求級數1.2.3+2.3.4+3.4.5+……n項之和
求級數〓之和
求級數a+(a+d)r+(a+2d)r²+……n項之和
附錄 問題之答及解法指南

Language Chinese
Publication date 民國23[1934]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
初等代數 組合 級數
中圖分類
InfoField
O122
載體形態
InfoField
201頁

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