## Differentiable Manifolds |
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```
matwuj@nus.edu.sg
```

- Lang, Serge,
*Introduction to differentiable manifolds*, Imprint New York , Interscience Publishers [1962] - Victor Guillemin and Alan Pollack,
*Differential Topology*, Prentice Hall, Inc, Englewood Cliffs, New Jersey [1974]. - Conlon, Lawrence,
*Differentiable manifolds : a first course / Lawrence Conlon*, Birkh8auser , [1993]. - Milnor, J.W., Topology from the differentiable viewpoint, The University Press of Virginia, Charlottesville, 1990.
- Jänich, Klaus.
*Vector analysis / Klaus Jänich ; translated by Leslie Kay.*Imprint New York : Springer, [c2001].

- Tangent Spaces, Vector Fields in
**R**^{n}and the Inverse Mapping Theorem - Topological Manifolds, Differentiable Manifolds,
Diffeomorphisms, Immersions, Submersions and Submanifolds
- Examples of Manifolds
- Fibre Bundles and Vector Bundles
- Tangent Bundles and Vector Fields
- Cotangent Bundles and Tensor Fields, Tensor Algebras and Exterior Algebras, Orientation of Manifolds, Integration on Manifolds
- Stokes' Theorem, DeRham Cohomology

Feedback on matters related to the course will be welcome. Please send it to matwuj@nus.edu.sg