目录__eol__第1 章 实数集与初等函数··················1__eol__1.1 实数集····································1__eol__1.1.1 集合及其运算························1__eol__1.1.2 映射···································3__eol__1.1.3 可数集································3__eol__1.1.4 实数集的性质························5__eol__1.1.5 戴德金原理···························8__eol__1.1.6 确界原理·····························8__eol__习题1.1····································· 10__eol__1.2 初等函数······························· 11__eol__1.2.1 函数的概念························· 11__eol__1.2.2 函数的一些特性··················· 12__eol__1.2.3 函数的运算························· 13__eol__1.2.4 基本初等函数······················ 14__eol__1.2.5 反函数及其存在条件·············· 18__eol__1.2.6 反三角函数························· 19__eol__*1.2.7 双曲函数和反双曲函数··········· 22__eol__*1.2.8 双曲函数与三角函数之间__eol__的联系······························ 24__eol__习题1.2····································· 24__eol__第2 章 数列极限····························· 27__eol__2.1 数列极限的概念······················ 27__eol__习题2.1····································· 30__eol__2.2 数列极限的性质······················ 31__eol__习题2.2····································· 35__eol__2.3 几类特殊的数列······················ 36__eol__2.3.1 无穷大数列与无穷小数列········ 36__eol__2.3.2 无穷大数列与无界数列··········· 36__eol__2.3.3 Stolz 定理·························· 38__eol__习题2.3 ···································· 40__eol__2.4 实数连续性定理····················· 41__eol__2.4.1 单调有界定理······················ 41__eol__2.4.2 闭区间套定理······················ 43__eol__2.4.3 Bolzano-Weierstrass 定理·········· 44__eol__2.4.4 柯西收敛准则······················ 45__eol__*2.4.5 有限覆盖定理······················ 47__eol__*2.4.6 聚点定理··························· 48__eol__习题2.4 ···································· 48__eol__*2.5 上极限与下极限···················· 50__eol__习题2.5 ···································· 54__eol__第3 章 函数极限与连续··················· 55__eol__3.1 函数极限的概念····················· 55__eol__3.1.1 函数在一点的极限················ 55__eol__3.1.2 函数在无穷远处的极限··········· 58__eol__习题3.1 ···································· 58__eol__3.2 函数极限的性质及运算············ 59__eol__3.2.1 函数极限的性质··················· 59__eol__3.2.2 函数极限的四则运算·············· 60__eol__3.2.3 复合函数的极限··················· 62__eol__习题3.2 ···································· 62__eol__3.3 函数极限的存在条件··············· 63__eol__3.3.1 函数极限与数列极限的关系······ 63__eol__3.3.2 两个重要极限······················ 65__eol__3.3.3 无穷大量与无穷小量·············· 67__eol__3.3.4 等价无穷小量代换求极限········· 69__eol__习题3.3····································· 71__eol__3.4 函数的连续···························· 73__eol__3.4.1 函数连续的概念··················· 73__eol__3.4.2 间断点及其分类··················· 74__eol__3.4.3 连续函数的局部性质·············· 78__eol__习题3.4····································· 78__eol__3.5 闭区间上连续函数的性质········· 79__eol__3.5.1 闭区间上连续函数的基本性质··· 79__eol__3.5.2 反函数的连续性··················· 82__eol__3.5.3 一致连续性························· 83__eol__习题3.5····································· 86__eol__第4 章 导数与微分·························· 89__eol__4.1 导数的概念···························· 89__eol__4.1.1 导数概念的引出··················· 89__eol__4.1.2 函数可导的条件与性质··········· 91__eol__习题4.1····································· 92__eol__4.2 求导法则······························· 94__eol__4.2.1 导数的四则运算法则·············· 94__eol__4.2.2 反函数求导法则··················· 96__eol__4.2.3 复合函数的导数——链式法则···· 97__eol__4.2.4 隐函数求导法则··················· 98__eol__4.2.5 参数方程求导法则················· 99__eol__习题4.2····································102__eol__4.3 函数的微分···························103__eol__4.3.1 可微的概念························103__eol__4.3.2 可微与可导的关系················104__eol__4.3.3 微分在函数近似计算中的应用··105__eol__4.3.4 微分的运算法则··················106__eol__习题4.3····································106__eol__4.4 高阶导数与高阶微分··············106__eol__4.4.1 高阶导数·························· 107__eol__4.4.2 高阶微分·························· 109__eol__4.4.3 复合函数的微分·················· 109__eol__习题4.4 ··································· 110__eol__第5 章 微分学基本定理及应用········· 112__eol__5.1 微分中值定理······················· 112__eol__5.1.1 极值