| 1. | 22. Februar (PDF) | how coordinates of a vector change under change of basis - contravariance; review of vector spaces and bases |
| 2. | 29. Februar (PDF) | how matrices of linear transformations change under change of basis; Einstein summation convention |
| 3. | 7. März (PDF) | linear forms, dual vector space, dual basis; how linear forms change under change of basis - covariance |
| 4. | 14. März (PDF) | linear forms - an example with computations; bilinear forms, tensor product of linear forms, basis for space of bilinear forms |
| 5. | 21. März (PDF) | blinear forms, components and matrix w.r.t. a basis, covariance; trilinear and k-linear forms; inner products, orthonormal basis |
| 6. | 28. März (PDF) | inner products, orthonormal bases; reciprocal basis, covariant coordinates |
| 7. | 4. April (PDF) | contravariance of reciprocal basis, raising and lowering indices; canonical identification between V and its dual given by metric |
| 8. | 18. April (PDF) | (2,0)-tensors, (p,q)-tensors; inertia tensor: angular velocity and kinetic energy |
| 9. | 25. April (PDF) | inertia tensor, moment of inertia, angular momentum; principal axes of inertia, principal moments of inertia, ellipsoid of inertia |
| 10. | 2. Mai (PDF) | tensor product of arbitrary tensors, tensor product of vector spaces; bilinear (or multilinear) functions viewed as linear functions on tensor products |
| 11. | 9. Mai (PDF) and text copies (PDF) | stress tensor, principal stresses and principal directions; hydrostatic pressure tensor and shear deformation tensor, invariants |
| 12. | 16. Mai (PDF) | strain tensor, rotation tensor, principal coefficients
and principal directions; uniform compression and shear deformation; elasticity tensor, Hooke's law |
| 13. | 23. Mai (PDF) | electrical conductivity tensor, heat conductivity tensor; contravariance of stress tensor |
| 14. | 30. Mai (PDF) | review / discussion / exercises |