Step 32 of 37
Calculus on curved spaces.
Topics, in order
- Smooth manifolds and maps
- Tangent and cotangent bundles
- Vector fields and flows
- Differential forms and Stokes' theorem
- Lie groups
- Riemannian metrics, connections, and curvature
Learn from
- Tu, An Introduction to Manifolds
- Lee, Introduction to Smooth Manifolds
- do Carmo, Riemannian Geometry
Move on when
You can state Stokes' theorem on a manifold and compute with differential forms.