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