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多元函数 第2版PDF|Epub|txt|kindle电子书版本下载
- （美）弗莱明著 著
- 出版社： 世界图书出版公司北京公司
- ISBN：9787510027307
- 出版时间：2010
- 标注页数：412页
- 文件大小：46MB
- 文件页数：419页
- 主题词：多变量－函数－英文
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图书目录
Chapter 1 Euclidean spaces1
1.1 The real number system2
1.2 Euclidean En5
1.3 Elementary geometry of En10
1.4 Basic topological notions in En14
1.5 Convex sets19
Chapter 2 Elementary topology of En28
2.1 Functions28
2.2 Limits and continuity of transformations31
2.3 Sequences in En37
2.4 Bolzano-Weierstrass theorem43
2.5 Relative neighborhoods,continuous transformations47
2.6 Topological spaces50
2.7 Connectedness56
2.8 Compactness60
2.9 Metric spaces62
2.10 Spaces of continuous functions67
2.11 Noneuclidean norms on En70
Chapter 3 Differentiation of real-valued functions76
3.1 Directional and partial derivatives76
3.2 Linear functions79
3.3 Differentiable functions82
3.4 Functions of class C(q)89
3.5 Relative extrema99
3.6 Convex and concave functions107
Chapter 4 Vector-valued functions of several variables119
4.1 Linear transformations119
4.2 Affine transformations125
4.3 Differentiable transformations128
4.4 Composition134
4.5 The inverse function theorem140
4.6 The implicit function theorem147
4.7 Manifolds153
4.8 The multiplier rule161
Chapter 5 Integration167
5.1 Intervals168
5.2 Measure170
5.3 Integrals over En181
5.4 Integrals over bounded sets186
5.5 Iterated integrals190
5.6 Integrals of continuous functions200
5.7 Change of measure under affine transformations206
5.8 Transformation of integrals209
5.9 Coordinate systems in En216
5.10 Measurable sets and functions;further properties222
5.11 Integrals：general definition,convergence theorems227
5.12 Differentiation under the integral sign237
5.13 Lp-spaces240
Chapter 6 Curves and line integrals245
6.1 Derivatives245
6.2 Curves in En247
6.3 Differential 1-forms253
6.4 Line integrals258
6.5 Gradient method265
6.6 Integrating factors;thermal systems268
Chapter 7 Exterior algebra and differential calculus275
7.1 Covectors and differential forms of degree 2276
7.2 Alternating multilinear functions283
7.3 Multicovectors287
7.4 Differential forms291
7.5 Multivectors295
7.6 Induced linear transformations306
7.7 Transformation law for differential forms309
7.8 The adjoint and codifferential311
7.9 Special results for n=3316
7.10 Integrating factors(continued)318
Chapter 8 Integration on manifolds321
8.1 Regular transformations322
8.2 Coordinate systems on manifolds329
8.3 Measure and integration on manifolds334
8.4 The divergence theorem340
8.5 Fluid flow350
8.6 Orientations353
8.7 Integrals of r-forms356
8.8 Stokess formula362
8.9 Regular transformations on submanifolds367
8.10 Closed and exact differential forms369
8.11 Motion ofa particle375
8.12 Motion of several particles380
Appendix 1 Axioms for a vector space383
Appendix 2 Mean value theorem;Taylors theorem385
Appendix 3 Review of Riemann integration386
Appendix 4 Monotone functions388
References389
Answers to problems391
Index405