| Area of Mathematics: | Algebra & Geometry (EAG) | ||
| Semester: | 8ο | ||
| Course ID: | 82201 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: |
Description
- Multilinear functions. Symmetric and antisymmetric multilinear functions.
- Tensor products of spaces and linear functions.
- Alternating and absolute tensors.
- Tensor algebras.
- Tangent and cotangent space of a differential form.
- Basic vector fields and basic 1-forms.
- k-th order differential forms.
- Outer product and outer differential.
- k-th order differential forms.
- Poincaré lemma.
- De Rham cohomology.
- Integration of differential forms.
- Stokes theorem.
Bibliography
- Spivak. Calculus on Manifolds. CRC Press, 1971.
- Do Carmo M., Riemannian Geometry, Birkhäuser Boston, Inc., Boston, MA, 1992.
- Jost J., Riemannian Geometry and Geometric Analysis. 6th Universitext Springer, Heidelberg, 2011.
- Flanders H., Differential Forms with Applications to the Physical Sciences, Dover, 1998.
