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(nèi)容包括極限與連續(xù)、導(dǎo)數(shù)與微分、微分 中值定理及導(dǎo)數(shù)應(yīng)用、不定積分、定積分及其應(yīng)用、微分方程；下冊內(nèi)容包括多元函數(shù)微分學(xué)、多元數(shù)量值函數(shù)積分學(xué)、多元向量值函數(shù)積分學(xué)、無窮級數(shù). 本書可作為高等學(xué)校理工科專業(yè)微積分課程的教材，也適合準(zhǔn)備考研的學(xué)生參考.
尤超教授，理學(xué)博士，現(xiàn)任哈爾濱工業(yè)大學(xué)數(shù)學(xué)學(xué)院數(shù)學(xué)教學(xué)研究中心副主任。主要研究方向?yàn)樗阕哟鷶?shù)，主講工科數(shù)學(xué)分析、數(shù)學(xué)競賽輔導(dǎo)等課程。主持、參與國家自然科學(xué)基金項(xiàng)目2項(xiàng)，主持、參與省部級教改項(xiàng)目2項(xiàng)。曾獲2022年寶鋼優(yōu)秀教師獎，2021年黑龍江省青年教學(xué)名師獎。
第 7 章 多元函數(shù)微分學(xué) ············································································································.1
7.1 多元函數(shù)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(shù) ···············································································································.2
7.1.3 多元函數(shù)的重極限與連續(xù) ························································································.3
7.1.4 多元函數(shù)的累次極限 ·······························································································.7
習(xí)題 7.1 ···························································································································.8
7.2 偏導(dǎo)數(shù)與高階偏導(dǎo)數(shù) ····································································································.9
7.2.1 偏導(dǎo)數(shù)的定義 ·········································································································.9
7.2.2 高階偏導(dǎo)數(shù) ··········································································································.11
習(xí)題 7.2 ·························································································································.14
7.3 全微分 ··························································································································.14
習(xí)題 7.3 ·························································································································.18
7.4 復(fù)合函數(shù)求導(dǎo)法 ··········································································································.19
習(xí)題 7.4 ·························································································································.25
7.5 隱函數(shù)求導(dǎo)法 ··············································································································.26
習(xí)題 7.5 ·························································································································.30
7.6 偏導(dǎo)數(shù)的幾何應(yīng)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(shù)全微分的幾何意義 ···················································································.35
習(xí)題 7.6 ·························································································································.35
7.7 多元函數(shù)的極值 ··········································································································.36
7.7.1 多元函數(shù)的無條件極值 ··························································································.36
7.7.2 條件極值與拉格朗日乘數(shù)法 ···················································································.42
習(xí)題 7.7 ·························································································································.46
7.8 方向?qū)?shù)與梯度 ··········································································································.46
7.8.1 場的基本概念 ·······································································································.46
7.8.2 方向?qū)?shù) ·············································································································.46
7.8.3 梯度 ····················································································································.49
習(xí)題 7.8 ·························································································································.51
綜合題 ··································································································································.52
第 8 章 多元數(shù)量值函數(shù)積分學(xué) ······························································································.53
8.1 黎曼積分 ·················································
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