《多元函数(第2版)》由世界图书出版公司出版。 |
作者：（美国）弗莱明（Wendell Fleming） .. << 查看详细 |
| chapter 1 euclidean spaces 1.1 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 e" 2.4 bolzano-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 i-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 muiticovectors 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 of r-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 |
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