| 1 | Learns the Lagrange Systems and Approximate Tangent Geometry, Homogen Lagrangians,Knows the Connections and Lagrangian Systems, Semi-Spraying and Lagrangian Systems. |
| 2 | Learns the Geometric Approximation of an Inverse Problem at Lagrange Dynamics, Knows the Legendre Transformation. |
| 3 | Identifies the Lagrangians Connected with Time, Dynamic Connections, Dynamic Connections and Lagrangians Connected with Time. |
| 4 | Knows the Variational Approximation. |