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中醫(yī)內(nèi)科學(xué)·全國中醫(yī)藥行業(yè)高等教育“十四五”規(guī)劃教材
高等數(shù)學(xué)辨析與精練(第2版) 版權(quán)信息
- ISBN：9787121487590
- 條形碼：9787121487590 ; 978-7-121-48759-0
- 裝幀：平塑
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>>
高等數(shù)學(xué)辨析與精練(第2版) 內(nèi)容簡介
本書為《高等數(shù)學(xué)》的同步輔導(dǎo)教材。全書按照一元函數(shù)微分學(xué)、微分方程、空間解析幾何與向量代數(shù)、 多元函數(shù)微分學(xué)和無窮級數(shù)的順序編排，每節(jié)包括四個部分：重要知識點、例題辨析、真題演練和真題演練解 析。本書的重點內(nèi)容為“重要知識點”和“例題辨析”。在“重要知識點”中系統(tǒng)梳理和凝練了高等數(shù)學(xué)重要 知識點和難點，以及常見解題方法的總結(jié)與注意要點。在“例題辨析”中結(jié)合編者多年的教學(xué)實踐，對學(xué)生學(xué) 習(xí)過程中常見的錯誤進(jìn)行剖析和總結(jié)，并通過相似的題目舉一反三，加深學(xué)生對內(nèi)容的理解。
高等數(shù)學(xué)辨析與精練(第2版) 目錄
第1 章 函數(shù)與極限····························································································1
1.1 映射與函數(shù)···························································································1
1.2 數(shù)列的極限···························································································4
1.3 函數(shù)的極限························································································.10
1.4 無窮小與無窮大··················································································.14
1.5 極限運算法則·····················································································.17
1.6 極限存在準(zhǔn)則和兩個重要極限·································································.23
1.7 無窮小的比較·····················································································.26
1.8 函數(shù)的連續(xù)性與間斷點·········································································.32
1.9 連續(xù)函數(shù)的運算及初等函數(shù)的連續(xù)性························································.36
1.10 閉區(qū)間上連續(xù)函數(shù)的性質(zhì)·····································································.38
第2 章 導(dǎo)數(shù)與微分·························································································.41
2.1 導(dǎo)數(shù)概念···························································································.41
2.2 函數(shù)的求導(dǎo)法則··················································································.48
2.3 高階導(dǎo)數(shù)···························································································.52
2.4 隱函數(shù)及由參數(shù)方程所確定函數(shù)的導(dǎo)數(shù)和相關(guān)變化率···································.55
2.5 函數(shù)的微分························································································.62
第3 章 微分中值定理與導(dǎo)數(shù)的應(yīng)用····································································.67
3.1 微分中值定理·····················································································.67
3.2 洛必達(dá)法則························································································.73
3.3 泰勒公式···························································································.79
3.4 函數(shù)的單調(diào)性與曲線的凹凸性·································································.86
3.5 函數(shù)的極值與*大值、*小值·································································.91
3.6 函數(shù)圖形的描繪··················································································.96
3.7 曲率·································································································.99
第4 章 不定積分····························································································102
4.1 不定積分的概念與性質(zhì)·········································································102
4.2 換元積分法························································································105
4.3 分部積分法························································································108
4.4 有理函數(shù)的積分··················································································113
第5 章 定積分·······························································································117
5.1 定積分的概念與性質(zhì)············································································117
5.2 微積分基本公式··················································································122
5.3 定積分的換元法和分部積分法·································································127
5.4 反常積分···························································································134
第6 章 定積分的應(yīng)用······················································································138
6.1 定積分在幾何學(xué)上的應(yīng)用······································································138
6.2 定積分在物理學(xué)上的應(yīng)用······································································145
第7 章 微分方程····························································································151
7.1 微分方程的基本概念············································································151
7.2 可分離變量的微分方程·········································································153
7.3 齊次方程···························································································157
7.4 一階線性微分方程·························
1.1 映射與函數(shù)···························································································1
1.2 數(shù)列的極限···························································································4
1.3 函數(shù)的極限························································································.10
1.4 無窮小與無窮大··················································································.14
1.5 極限運算法則·····················································································.17
1.6 極限存在準(zhǔn)則和兩個重要極限·································································.23
1.7 無窮小的比較·····················································································.26
1.8 函數(shù)的連續(xù)性與間斷點·········································································.32
1.9 連續(xù)函數(shù)的運算及初等函數(shù)的連續(xù)性························································.36
1.10 閉區(qū)間上連續(xù)函數(shù)的性質(zhì)·····································································.38
第2 章 導(dǎo)數(shù)與微分·························································································.41
2.1 導(dǎo)數(shù)概念···························································································.41
2.2 函數(shù)的求導(dǎo)法則··················································································.48
2.3 高階導(dǎo)數(shù)···························································································.52
2.4 隱函數(shù)及由參數(shù)方程所確定函數(shù)的導(dǎo)數(shù)和相關(guān)變化率···································.55
2.5 函數(shù)的微分························································································.62
第3 章 微分中值定理與導(dǎo)數(shù)的應(yīng)用····································································.67
3.1 微分中值定理·····················································································.67
3.2 洛必達(dá)法則························································································.73
3.3 泰勒公式···························································································.79
3.4 函數(shù)的單調(diào)性與曲線的凹凸性·································································.86
3.5 函數(shù)的極值與*大值、*小值·································································.91
3.6 函數(shù)圖形的描繪··················································································.96
3.7 曲率·································································································.99
第4 章 不定積分····························································································102
4.1 不定積分的概念與性質(zhì)·········································································102
4.2 換元積分法························································································105
4.3 分部積分法························································································108
4.4 有理函數(shù)的積分··················································································113
第5 章 定積分·······························································································117
5.1 定積分的概念與性質(zhì)············································································117
5.2 微積分基本公式··················································································122
5.3 定積分的換元法和分部積分法·································································127
5.4 反常積分···························································································134
第6 章 定積分的應(yīng)用······················································································138
6.1 定積分在幾何學(xué)上的應(yīng)用······································································138
6.2 定積分在物理學(xué)上的應(yīng)用······································································145
第7 章 微分方程····························································································151
7.1 微分方程的基本概念············································································151
7.2 可分離變量的微分方程·········································································153
7.3 齊次方程···························································································157
7.4 一階線性微分方程·························
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