本書主要針對拔尖創(chuàng)新人才培養(yǎng)而編寫，分上、下兩冊. 上冊內容包括極限與連續(xù)、導數與微分、微分 中值定理及導數應用、不定積分、定積分及其應用、微分方程；下冊內容包括多元函數微分學、多元數量值函數積分學、多元向量值函數積分學、無窮級數. 本書可作為高等學校理工科專業(yè)微積分課程的教材，也適合準備考研的學生參考.
尤超教授，理學博士，現任哈爾濱工業(yè)大學數學學院數學教學研究中心副主任。主要研究方向為算子代數，主講工科數學分析、數學競賽輔導等課程。主持、參與國家自然科學基金項目2項，主持、參與省部級教改項目2項。曾獲2022年寶鋼優(yōu)秀教師獎，2021年黑龍江省青年教學名師獎。
第 7 章 多元函數微分學 ············································································································.1
7.1 多元函數的基本概念及其極限 ·····················································································.1
7.1.1 n 維歐式空間 ········································································································.1
7.1.2 多元函數 ···············································································································.2
7.1.3 多元函數的重極限與連續(xù) ························································································.3
7.1.4 多元函數的累次極限 ·······························································································.7
習題 7.1 ···························································································································.8
7.2 偏導數與高階偏導數 ····································································································.9
7.2.1 偏導數的定義 ·········································································································.9
7.2.2 高階偏導數 ··········································································································.11
習題 7.2 ·························································································································.14
7.3 全微分 ··························································································································.14
習題 7.3 ·························································································································.18
7.4 復合函數求導法 ··········································································································.19
習題 7.4 ·························································································································.25
7.5 隱函數求導法 ··············································································································.26
習題 7.5 ·························································································································.30
7.6 偏導數的幾何應用 ······································································································.31
7.6.1 空間曲線的切線與法平面 ······················································································.31
7.6.2 曲面的切平面與法線 ·····························································································.33
7.6.3 二元函數全微分的幾何意義 ···················································································.35
習題 7.6 ·························································································································.35
7.7 多元函數的極值 ··········································································································.36
7.7.1 多元函數的無條件極值 ··························································································.36
7.7.2 條件極值與拉格朗日乘數法 ···················································································.42
習題 7.7 ·························································································································.46
7.8 方向導數與梯度 ··········································································································.46
7.8.1 場的基本概念 ·······································································································.46
7.8.2 方向導數 ·············································································································.46
7.8.3 梯度 ····················································································································.49
習題 7.8 ·························································································································.51
綜合題 ··································································································································.52
第 8 章 多元數量值函數積分學 ······························································································.53
8.1 黎曼積分 ·················································
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