| ÖÇ1 | Learns the concept of a manifold. |
| ÖÇ2 | Learns Euclidean space as a manifold. |
| ÖÇ3 | Learns the concepts of tangent vector, tangent space, vector field, and space of vector fields in Euclidean space. |
| ÖÇ4 | Learns the concepts of directional derivative, cotangent space, and a form. |
| ÖÇ5 | Learns the differential of a transformation, derivative transformation, and Jacobian. |
| ÖÇ6 | Learns submanifolds and manifold transformations. |