Lecture Notes on Differentiable Manifolds
نویسنده
چکیده
1. Tangent Spaces, Vector Fields in R and the Inverse Mapping Theorem 1 1.1. Tangent Space to a Level Surface 1 1.2. Tangent Space and Vectors Fields on R 2 1.3. Operator Representations of Vector Fields 3 1.4. Integral Curves 4 1.5. Implicitand Inverse-Mapping Theorems 5 2. Topological and Differentiable Manifolds 9 3. Diffeomorphisms, Immersions, Submersions and Submanifolds 9 4. Fibre Bundles and Vector Bundles 9 5. Tangent Bundles and Vector Fields 9 6. Cotangent Bundles and Tensor Fields 9 7. Orientation of Manifolds 9 8. Tensor Algebras and Exterior Algebras 9 9. DeRham Cohomology 9 10. Integration on Manifolds 9 11. Stokes’ Theorem 9 References 9
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