| 1 | To teach the concept of manifold. |
| 2 | To ıntroduce as a manifold to Euclidean space. |
| 3 | To teach topological and differentiable manifolds |
| 4 | To introduce the concepts of tangent vector, tangent space, vector fields, vector fields in Euclidean space |
| 5 | To introduce the concepts of directional derivative, cotangent space, in a form |
| 6 | To teach a differentation of a map and jakobian |