微积分（下）

图书标准信息

• 作者 尤超
• 出版社 电子工业出版社
• 出版时间 2023-02
• 版次 1
• ISBN 9787121450051
• 定价 52.00元
• 装帧 其他
• 页数 232页

【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.

【作者简介】

尤超教授，理学博士，现任哈尔滨工业大学数学学院数学教学研究中心副主任。主要研究方向为算子代数，主讲工科数学分析、数学竞赛辅导等课程。主持、参与国家自然科学基金项目2项，主持、参与省部级教改项目2项。曾获2022年宝钢优秀教师奖，2021年黑龙江省青年教学名师奖。

【目录】

第 7 章 多元函数微分学 ············································································································.1

7.1 多元函数的基本概念及其极限 ·····················································································.1 

7.1.1 n 维欧式空间 ········································································································.1

7.1.2 多元函数 ···············································································································.2

7.1.3 多元函数的重极限与连续 ························································································.3

7.1.4 多元函数的累次极限 ·······························································································.7

习题 7.1 ···························································································································.8

7.2 偏导数与高阶偏导数 ····································································································.9 

7.2.1 偏导数的定义 ·········································································································.9

7.2.2 高阶偏导数 ··········································································································.11

习题 7.2 ·························································································································.14

7.3 全微分 ··························································································································.14

习题 7.3 ·························································································································.18

7.4 复合函数求导法 ··········································································································.19 

习题 7.4 ·························································································································.25

7.5 隐函数求导法 ··············································································································.26 

习题 7.5 ·························································································································.30

7.6 偏导数的几何应用 ······································································································.31 

7.6.1 空间曲线的切线与法平面 ······················································································.31

7.6.2 曲面的切平面与法线 ·····························································································.33

7.6.3 二元函数全微分的几何意义 ···················································································.35

习题 7.6 ·························································································································.35

7.7 多元函数的极值 ··········································································································.36 

7.7.1 多元函数的无条件极值 ··························································································.36

7.7.2 条件极值与拉格朗日乘数法 ···················································································.42

习题 7.7 ·························································································································.46

7.8 方向导数与梯度 ··········································································································.46 

7.8.1 场的基本概念 ·······································································································.46

7.8.2 方向导数 ·············································································································.46

7.8.3 梯度 ····················································································································.49

习题 7.8 ·························································································································.51

综合题 ··································································································································.52 

第 8 章 多元数量值函数积分学 ······························································································.53

8.1 黎曼积分 ·················································