Differential Geometry
A 14-module path through differential geometry, in study order from foundations to the frontier.
Modules
- Regular Curves and Arc Length
- Curvature of Space Curves
- The Frenet-Serret Frame
- Fundamental Theorem of Space Curves
- Regular Surfaces and Parametrizations
- The Tangent Plane and Differential of a Map
- The First Fundamental Form
- The Gauss Map
- The Second Fundamental Form
- Gaussian and Mean Curvature
- Theorema Egregium
- Geodesics on Surfaces
- The Gauss-Bonnet Theorem
- Manifolds and Tangent Spaces