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· 제목 : Introduction to Smooth Manifolds (Paperback, 2, 2012) 
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 미분기하학
· ISBN : 9781489994752
· 쪽수 : 708쪽
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 미분기하학
· ISBN : 9781489994752
· 쪽수 : 708쪽
목차
Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index
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