| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| MATHEMATICS | ||
Course unit
SYMPLECTIC MECHANICS
SC02119743, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
SYMPLECTIC MECHANICS
SC02119743, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Information on the course unit
| Degree course |
Second cycle degree in MATHEMATICS SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20 |
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|---|---|---|
| Degree course track | GENERALE [010PD] | |
| Number of ECTS credits allocated | 6.0 | |
| Type of assessment | Mark | |
| Course unit English denomination | SYMPLECTIC MECHANICS | |
| Website of the academic structure | http://matematica.scienze.unipd.it/2019/laurea_magistrale | |
| Department of reference | Department of Mathematics | |
| Mandatory attendance | No | |
| Language of instruction | English | |
| Branch | PADOVA | |
| Single Course unit | The Course unit can be attended under the option Single Course unit attendance | |
| Optional Course unit | The Course unit can be chosen as Optional Course unit |
Lecturers
| Teacher in charge | FRANCO CARDIN | MAT/07 |
|---|
Mutuated
| Course unit code | Course unit name | Teacher in charge | Degree course code |
|---|---|---|---|
| SC02119743 | SYMPLECTIC MECHANICS | FRANCO CARDIN | SC1172 |
ECTS: details
| Type | Scientific-Disciplinary Sector | Credits allocated | |
|---|---|---|---|
| Core courses | MAT/07 | Mathematical Physics | 6.0 |
Course unit organization
| Period | First semester |
|---|---|
| Year | 1st Year |
| Teaching method | frontal |
| Type of hours | Credits | Teaching hours |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| Practice | 3.0 | 24 | 51.0 | No turn |
| Lecture | 3.0 | 24 | 51.0 | No turn |
| Start of activities | 30/09/2019 |
|---|---|
| End of activities | 18/01/2020 |
| Show course schedule | 2019/20 Reg.2011 course timetable |
| Prerequisites: | Elementary Calculus and Geometry |
| Target skills and knowledge: | Differential and Symplectic Geometry. Global Hamiltonian Mechanics. Geometric theory of the Hamilton-Jacobi equation. Symplectic Topology. Calculus of Variations: Conjugate Points, Morse Index, Lusternik-Schnirelman Theory for the existence of critical points. |
| Examination methods: | Written. |
| Assessment criteria: | Assessment of learning theoretical and practical notions on the course. |
| Course unit contents: | Essential of Differential Geometry and Exterior Differential Calculus.
Cohomology. Riemannian manifolds: Existence of metrics, Whitney theorem. Symplectic Geometry: Symplectic manifolds. Introduction and developments of Hamiltonian Mechanics on symplectic manifolds. Local and global parameterization of the Lagrangian submanifolds and their generating functions. Theorem of Maslov-H\"ormander. Hamilton-Jacobi equation, its geometrical solutions and links to the Calculus of Variations. Conjugate points theory in calculus of variations. Relative cohomology and Lusternik-Schnirelman theory. Introduction to Symplectic Topology: existence and classification of critical points of functions and applications to generating functions of Lagrangian submanifolds. The min-max solution of Hamilton-Jacobi equation. Symplectic Topology by Viterbo: towards the solution of the Arnol'd conjecture. Morse theory. |
| Planned learning activities and teaching methods: | lectures and tutorials |
| Additional notes about suggested reading: | F. Cardin: Elementary Symplectic Topology and Mechanics, Springer 2015 |
| Textbooks (and optional supplementary readings) |
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