Functions of several variables = 多元函数 / 2nd ed.

　　Chapter 1 Euclidean spaces
　　 1.l The real number system
　　 1.2 Euclidean En
　　 1.3 Elementary geometry of En
　　 1.4 Basic topological notions in En
　　 *1.5 Convex sets
　　Chapter 2 Elementary topology of En
　　 2.1 Functions
　　 2.2 Limits and continuity of transformations
　　 2.3 Sequences in En
　　 2.4 Bo|zano-Weierstrass theorem
　　 2.5 Relative neighborhoods, continuous transformations
　　 2.6 Topological spaces
　　 2.7 Connectedness
　　 2.8 Compactness
　　 2.9 Metric spaces
　　 2.10 Spaces of continuous functions
　　 *2.11 Noneuclidean norms on En
　　Chapter 3 Differentiation of real-valued functions
　　 3.1 Directional and partial derivatives
　　 3.2 Linear functions
　　 3.3 Differentiable functions
　　 3.4 Functions of class C（q）
　　 3.5 Relative extrema
　　 *3.6 Convex and concave functions
　　Chapter 4 Vector-valued functions of several variables
　　 4.1 Linear transformations
　　 4.2 Affine transformations
　　 4.3 Differentiable transformations
　　 4.4 Composition
　　 4.5 The inverse function theorem
　　 4.6 The implicit function theorem
　　 4.7 Manifolds
　　 4.8 The multiplier rule
　　Chapter 5 Integration
　　 5.1 Intervals
　　 5.2 Measure
　　 5.3 Integrals over En
　　 5.4 Integrals over bounded sets
　　 5.5 Iterated integrals
　　 5.6 Integrals of continuous functions
　　 5.7 Change of measure under affine transformations
　　 5.8 Transformation of integrals
　　 5.9 Coordinate systems in En
　　 5.10 Measurable sets and functions; further properties
　　 5.11 Integrals: general definition, convergence theorems
　　 5.12 Differentiation under the integral sign
　　 5.13 LP-spaces
　　Chapter 6 Curves and line integrals
　　 6.1 Derivatives
　　 6.2 Curves in En
　　 6.3 Differential l-forms
　　 6.4 Line integrals
　　 *6.5 Gradient method
　　 *6.6 Integrating factors; thermal systems
　　Chapter 7 Exterior algebra and differential calculus
　　 7.1 Covectors and differential forms of degree 2
　　 7.2 Alternating multilinear functions
　　 7.3 Multicovectors
　　 7.4 Differential forms
　　 7.5 Multivectors
　　 7.6 Induced linear transformations
　　 7.7 Transformation law for differential forms
　　 7.8 The adjoint and codifferential
　　 *7.9 Special results for n=3
　　 *7.10 Integrating factors （continued）
　　Chapter 8 Integration on manifolds
　　 8.1 Regular transformations
　　 8.2 Coordinate systems on manifolds
　　 8.3 Measure and integration on manifolds
　　 8.4 The divergence theorem
　　 *8.5 Fluid flow
　　 8.6 Orientations
　　 8.7 Integrals oft-forms
　　 8.8 Stokes's formula
　　 8.9 Regular transformations on submanifolds
　　 8.10 Closed and exact differential forms
　　 8.11 Motion of a particle
　　 8.12 Motion of several particles
　　Appendix 1 Axioms for a vector space
　　Appendix 2 Mean value theorem; Taylor's theorem
　　Appendix 3 Review of Riemann integration
　　Appendix 4 Monotone functions
　　References
　　Answers to problems
　　Index