微積分原理（上）

定　價：￥69.00

作　者：	崔建蓮
出版社：	電子工業(yè)出版社
叢編項：
標　簽：	暫缺

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當當網(wǎng) (￥58.60)

ISBN：	9787121458392	出版時間：	2023-07-01	包裝：	平塑
開本：		頁數(shù)：		字數(shù)：

內(nèi)容簡介

　　微積分是理工科高等學校非數(shù)學類專業(yè)最基礎、重要的一門核心課程。許多后繼數(shù)學課程及物理和各種工程學課程都是在微積分課程的基礎上展開的，因此學好這門課程對每一位理工科學生來說都非常重要。本書在傳授微積分知識的同時，注重培養(yǎng)學生的數(shù)學思維、語言邏輯和創(chuàng)新能力，弘揚數(shù)學文化，培養(yǎng)科學精神。本套教材分上、下兩冊。上冊內(nèi)容包括實數(shù)集與初等函數(shù)、數(shù)列極限、函數(shù)極限與連續(xù)、導數(shù)與微分、微分學基本定理及應用、不定積分、定積分、廣義積分和常微分方程。下冊內(nèi)容包括多元函數(shù)的極限與連續(xù)、多元函數(shù)微分學及其應用、重積分、曲線積分、曲面積分、數(shù)項級數(shù)、函數(shù)項級數(shù)、傅里葉級數(shù)和含參積分。

作者簡介

　　崔建蓮，清華大學數(shù)學系副教授，主要研究方向為算子代數(shù)、算子理論及在量子信息中的應用，發(fā)表學術論文60多篇，SCI收錄50多篇。

圖書目錄

目錄
第1 章實數(shù)集與初等函數(shù)··················1
1.1 實數(shù)集····································1
1.1.1 集合及其運算························1
1.1.2 映射···································3
1.1.3 可數(shù)集································3
1.1.4 實數(shù)集的性質(zhì)························5
1.1.5 戴德金原理···························8
1.1.6 確界原理·····························8
習題1.1····································.10
1.2 初等函數(shù)······························.11
1.2.1 函數(shù)的概念························.11
1.2.2 函數(shù)的一些特性··················.12
1.2.3 函數(shù)的運算························.13
1.2.4 基本初等函數(shù)·····················.14
1.2.5 反函數(shù)及其存在條件·············.18
1.2.6 反三角函數(shù)························.19
*1.2.7 雙曲函數(shù)和反雙曲函數(shù)··········.22
*1.2.8 雙曲函數(shù)與三角函數(shù)之間
的聯(lián)系·····························.24
習題1.2····································.24
第2 章數(shù)列極限····························.27
2.1 數(shù)列極限的概念·····················.27
習題2.1····································.30
2.2 數(shù)列極限的性質(zhì)·····················.31
習題2.2····································.35
2.3 幾類特殊的數(shù)列·····················.36
2.3.1 無窮大數(shù)列與無窮小數(shù)列·······.36
2.3.2 無窮大數(shù)列與無界數(shù)列··········.36
2.3.3 Stolz 定理·························.38
習題2.3 ···································.40
2.4 實數(shù)連續(xù)性定理····················.41
2.4.1 單調(diào)有界定理·····················.41
2.4.2 閉區(qū)間套定理·····················.43
2.4.3 Bolzano-Weierstrass 定理·········.44
2.4.4 柯西收斂準則·····················.45
*2.4.5 有限覆蓋定理·····················.47
*2.4.6 聚點定理··························.48
習題2.4 ···································.48
*2.5 上極限與下極限···················.50
習題2.5 ···································.54
第3 章函數(shù)極限與連續(xù)··················.55
3.1 函數(shù)極限的概念····················.55
3.1.1 函數(shù)在一點的極限···············.55
3.1.2 函數(shù)在無窮遠處的極限··········.58
習題3.1 ···································.58
3.2 函數(shù)極限的性質(zhì)及運算···········.59
3.2.1 函數(shù)極限的性質(zhì)··················.59
3.2.2 函數(shù)極限的四則運算·············.60
3.2.3 復合函數(shù)的極限··················.62
習題3.2 ···································.62
3.3 函數(shù)極限的存在條件··············.63
3.3.1 函數(shù)極限與數(shù)列極限的關系·····.63
3.3.2 兩個重要極限·····················.65
3.3.3 無窮大量與無窮小量·············.67
3.3.4 等價無窮小量代換求極限········.69
習題3.3····································.71
3.4 函數(shù)的連續(xù)···························.73
3.4.1 函數(shù)連續(xù)的概念··················.73
3.4.2 間斷點及其分類··················.74
3.4.3 連續(xù)函數(shù)的局部性質(zhì)·············.78
習題3.4····································.78
3.5 閉區(qū)間上連續(xù)函數(shù)的性質(zhì)········.79
3.5.1 閉區(qū)間上連續(xù)函數(shù)的基本性質(zhì)··.79
3.5.2 反函數(shù)的連續(xù)性··················.82
3.5.3 一致連續(xù)性························.83
習題3.5····································.86
第4 章導數(shù)與微分·························.89
4.1 導數(shù)的概念···························.89
4.1.1 導數(shù)概念的引出··················.89
4.1.2 函數(shù)可導的條件與性質(zhì)··········.91
習題4.1····································.92
4.2 求導法則······························.94
4.2.1 導數(shù)的四則運算法則·············.94
4.2.2 反函數(shù)求導法則··················.96
4.2.3 復合函數(shù)的導數(shù)——鏈式法則···.97
4.2.4 隱函數(shù)求導法則··················.98
4.2.5 參數(shù)方程求導法則················.99
習題4.2····································102
4.3 函數(shù)的微分···························103
4.3.1 可微的概念························103
4.3.2 可微與可導的關系················104
4.3.3 微分在函數(shù)近似計算中的應用··105
4.3.4 微分的運算法則··················106
習題4.3····································106
4.4 高階導數(shù)與高階微分··············106
4.4.1 高階導數(shù)·························.107
4.4.2 高階微分·························.109
4.4.3 復合函數(shù)的微分·················.109
習題4.4 ··································.110
第5 章微分學基本定理及應用········.112
5.1 微分中值定理······················.112
5.1.1 極值的概念與費馬定理·········.112
5.1.2 微分中值定理····················.113
習題5.1 ··································.118
5.2 洛必達法則··························.120
5.2.1 0
0
型不定式極限·················.120
5.2.2 ∞
∞
型不定式極限················.123
5.2.3 其他類型不定式極限············.125
習題5.2 ··································.126
5.3 泰勒公式及應用···················.127
5.3.1 泰勒公式·························.128
5.3.2 基本初等函數(shù)的展開式·········.130
5.3.3 泰勒公式的應用·················.134
習題5.3 ··································.138
5.4 單調(diào)性與極值······················.140
5.4.1 函數(shù)的單調(diào)性····················.140
5.4.2 函數(shù)取極值的條件··············.142
習題5.4 ··································.145
5.5 函數(shù)的凸性與函數(shù)作圖··········.147
5.5.1 函數(shù)的凸性······················.147
5.5.2 曲線的漸近性····················.152
5.5.3 函數(shù)作圖·························.153
習題5.5 ··································.155
*5.6 方程求根的牛頓迭代公式·····.155
第6 章不定積分···························.160
6.1 原函數(shù)與不定積分················.160
6.1.1 原函數(shù)與6