| 1 | Affine space, Euclidean space and Euclidean frame. | [1] p. 1-8 |
| 2 | Topological manifolds and differentiable manifolds. | [1] p. 11-29 |
| 3 | Tangent vectors, tangent spaces and vector fields | [1] p. 31-40 |
| 4 | Directional derivative, integral curves and their relation to sustainable engineering. | [1] p. 40-52 |
| 5 | integral curves, Lie bracket | [1] p. 52-67 |
| 6 | 1-forms and k-forms | [1] p. 69-81 |
| 7 | Gradient, Divergence and Rotational functions | [1] s. 81-87 |
| 8 | Midterm exam, A differentation of a map. | [1] p. 92-95 |
| 9 | A differentation of a map, Derivative transformations, Jakobian | [1] p. 95-104 |
| 10 | Transformations of Euclidean spaces | [1] p. 95-104 |
| 11 | sub-manifolds, Among transformations of manifolds | [1] p. 104-113 |
| 12 | immersion and imbedding, | [1] p. 104-113 |
| 13 | Tensors and tensor spaces, | [1] p. 113-123 |
| 14 | Exterior product in differential forms | [1] . 124-152 |