Learning Outcomes:
1. Expalin the concept of a tensor over a vector space.
2. Describe the construction of the dual basis and its transformation properties.
3. Explain the concept of manifolds
4. Explain the constuction of vector and tensor fields on a manifold.
5. Describe the pull back and push forward of appropriate tensors.
6. Expalin the concept of a one-parameter family of diffeomorphisms and the Lie derivative.
7. Explain the concept of a connection and the corresponding differentiation of tensor fields.
8. Explain the concepts of parallel transport and curvature.
9. Calculate the equations of geodesic motion.
10. Compute the curvature of a manifold.