| Lecture | About | File |
|---|---|---|
| Lecture 1 | Notions from Set theory | lecture-01.pdf |
| Lecture 2 | Group-like structures | lecture-02.pdf |
| Lecture 3 | Group homomorphisms. Rings | lecture-03.pdf |
| Lecture 4 | Modules over commutative rings with unity | lecture-04.pdf |
| Lecture 5 | Dimension of free modules. Module homomorphisms | lecture-05.pdf |
| Lecture 6 | Dual modules and dual maps. Bilinear maps | lecture-06.pdf |
| Lecture 7 | Tensor Product. Algebras | lecture-07.pdf |
| Lecture 8 | Exterior Algebra. Determinants | lecture-08.pdf |
| Lecture 9 | Open and closed sets. Smooth maps and immersions | lecture-09.pdf |
| Lecture 10 | Manifolds. Smooth maps. Vector fields. Differential forms. Exterior derivative | lecture-10.pdf |
| Lecture 11 | Pullback. Trace of forms. Orientation. Integration on manifolds. Stokes–Cartan theorem | lecture-11.pdf |
| Lecture 12 | Metric tensor. Riemannian manifolds. Musical isomorphisms. Volume form. Hodge star. | lecture-12.pdf |
| Lecture 13 | Manifold measures. Inner product. Transport phenomena in exterior calculus. | lecture-13.pdf | Lecture 14 | Chain and cochain complexes. Boundary and coboundary operators. de Rham map. | lecture-14.pdf |