MP10 · Tensors & differential geometry
A 19-module path through mp10 · tensors & differential geometry, in study order from foundations to the frontier.
Modules
- Tensor Algebra and the Tensor Product
- Covariant and Contravariant Tensors
- The Metric Tensor
- Raising and Lowering Indices
- Tensor Contraction and the Trace
- Manifolds and Tangent Spaces
- The Covariant Derivative
- Christoffel Symbols and Affine Connections
- Parallel Transport and Geodesics
- Differential Forms
- Exterior Calculus and the Exterior Derivative
- Hodge Star and the Codifferential
- The Riemann Curvature Tensor
- Ricci Tensor, Ricci Scalar, and the Einstein Tensor
- Lie Derivatives and Killing Vectors
- Bianchi Identities and Conservation Laws
- Geodesic Deviation and Tidal Forces
- Fiber Bundles and Gauge Connections
- Curvature Forms and Characteristic Classes