| Area of Mathematics: | Analysis (EA) | ||
| Semester: | 6ο | ||
| Course ID: | 62103 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Tsirivas Nikolaos | ||
Description
- Differentiability of several variables functions. Inverse function theorem and implicit function theorem , higher order derivatives.
- Surfaces in Rn, Sard theorem.
- Partitions of unity. Change of variables formula in multiple integrals.
- Differential forms in Rn and on surfaces, Poincaré Lemma, ∂ –equation.
- Stokes’ theorem, volume element , Gauss Divergence Theorem, degree theory, examples of de Rham cohomology. Applications.
Bibliography
- M.Spivak , Calculus on Manifolds , A Modern Approach to Classical Theorems of Advanced Calculus ,Addison-Wesley , 1965.
- Sternberg , Lectures on Differential Geometry , Prentice Hall , Englewood Cliffs , New Jersey , 1964 .
