内容介绍
本书分上、下两册。上册聚焦一元函数微积分学,涵盖函数、极限与连续、导数与微分、微分的应用、不定积分、定积分及其应用、微分方程等内容;下册围绕多元函数微积分学展开,内容包括多元函数微分学、黎曼积分、向量微积分、无穷级数等。本书每章均配有不同难度的大量习题,供读者巩固所学、强化训练。
本书适合高等学校理工科专业学生(尤其是英语基础扎实的学生及海外留学生)学习微积分课程使用,也可作为工科硕士研究生入学考试的复习资料以及工程相关从业者的参考书。
大学微积分(下)(英文版)
目录
●Chapter 8 Differentiation of Multivariable Functions 1
8.1 Basic Concepts of Multivariable Functions 1
8.2 Partial Derivatives and Higher Derivatives 6
8.3 Total Differentials and Linear Approximations 13
8.4 The Chain Rule 17
8.5 Implicit Differentiation 20
8.6 Geometric Applications of Partial Derivatives 26
8.7 Maximum and Minimum Values 33
8.8 Directional Derivatives and the Gradient Vector 43
Exercises 8 48
Chapter 9 Riemann Integrals 58
9.1 Basic Concepts of Riemann Integrals 58
9.2 Double Integrals 63
9.3 Triple Integrals 75
9.4 Line Integrals with Respect to Arc Length 84
9.5 Surface Integrals with Respect to Surface Area 88
9.6 Applications of Riemann Integrals 93
9.7 Change of Variables in Multiple Integrals 98
Exercises 9 103
Chapter 10 Vector Calculus 111
10.1 Line Integrals of Vector Fields 112
10.2 Green’s Theorem 119
10.3 Independence of Path, Conservative Fields and Exact Differential Equations 124
10.4 Surface Integrals of Vector Fields 134
10.5 Gauss’s Theorem, Flux and Divergence 142
10.6 Stokes’ Theorem, Circulation and Rotation 149
Exercises 10 157
Chapter 11 Infinite Series 167
11.1 Convergence and Divergence of Numerical Series 168
11.2 Series with Non-Negative Terms 177
11.3 Series with Arbitrary Terms, Absolute Convergence 186
11.4 Series with Function Terms, Uniform Convergence 192
11.5 Power Series 201
11.6 Representations of Functions as Power Series and Summation of Power Series 210
11.7 Applications of Power Series 223
11.8 Fourier Series 228
Exercises 11 240
内容介绍
本书分上、下两册。上册聚焦一元函数微积分学,涵盖函数、极限与连续、导数与微分、微分的应用、不定积分、定积分及其应用、微分方程等内容;下册围绕多元函数微积分学展开,内容包括多元函数微分学、黎曼积分、向量微积分、无穷级数等。本书每章均配有不同难度的大量习题,供读者巩固所学、强化训练。
本书适合高等学校理工科专业学生(尤其是英语基础扎实的学生及海外留学生)学习微积分课程使用,也可作为工科硕士研究生入学考试的复习资料以及工程相关从业者的参考书。
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