- 电子工业出版社
- 9787121450051
- 1-3
- 466077
- 48253753-7
- 平塑
- 16开
- 2023-07
- 371
- 232
- 数学
- 本科
内容简介
本书主要针对拔尖创新人才培养而编写,分上、下两册. 上册内容包括极限与连续、导数与微分、微分 中值定理及导数应用、不定积分、定积分及其应用、微分方程;下册内容包括多元函数微分学、多元数量值函数积分学、多元向量值函数积分学、无穷级数. 本书可作为高等学校理工科专业微积分课程的教材,也适合准备考研的学生参考.
目录
第 7 章 多元函数微分学 ············································································································· 1__eol__7.1 多元函数的基本概念及其极限 ······················································································ 1 __eol__7.1.1 n 维欧式空间 ········································································································· 1__eol__7.1.2 多元函数 ················································································································ 2__eol__7.1.3 多元函数的重极限与连续 ························································································· 3__eol__7.1.4 多元函数的累次极限 ································································································ 7__eol__习题 7.1 ···························································································································· 8__eol__7.2 偏导数与高阶偏导数 ····································································································· 9 __eol__7.2.1 偏导数的定义 ·········································································································· 9__eol__7.2.2 高阶偏导数 ··········································································································· 11__eol__习题 7.2 ·························································································································· 14__eol__7.3 全微分 ··························································································································· 14__eol__习题 7.3 ·························································································································· 18__eol__7.4 复合函数求导法 ··········································································································· 19 __eol__习题 7.4 ·························································································································· 25__eol__7.5 隐函数求导法 ··············································································································· 26 __eol__习题 7.5 ·························································································································· 30__eol__7.6 偏导数的几何应用 ······································································································· 31 __eol__7.6.1 空间曲线的切线与法平面 ······················································································· 31__eol__7.6.2 曲面的切平面与法线 ······························································································ 33__eol__7.6.3 二元函数全微分的几何意义 ···················································································· 35__eol__习题 7.6 ·························································································································· 35__eol__7.7 多元函数的极值 ··········································································································· 36 __eol__7.7.1 多元函数的无条件极值 ··························································································· 36__eol__7.7.2 条件极值与拉格朗日乘数法 ···················································································· 42__eol__习题 7.7 ·························································································································· 46__eol__7.8 方向导数与梯度 ··········································································································· 46 __eol__7.8.1 场的基本概念 ········································································································ 46__eol__7.8.2 方向导数 ·············································································································· 46__eol__7.8.3 梯度 ····················································································································· 49__eol__习题 7.8 ·························································································································· 51__eo