Hamiltonian mechanics

Uitgebreide vaknaam	Hamiltonian mechanics
Leerdoelen	At the end of the course, the student is able to: 1. understand classical mechanics from the Newtonian, the Lagrangian and Hamiltonian point of view in terms calculus on manifolds 2. understand symplectic geometry and how it relates to the description of mechanical systems 3. understand the concept of integrable system and its centrality in perturbation theory 4. deal with concrete mechanical examples in this way, from modelling to describing the geometry of the solutions 5. deepen and broad the mathematical background
Omschrijving	Mathematical aspects of classical mechanics will be developed via Newtonian and Lagrangian systems to the world of Hamiltonian systems, which most naturally live on symplectic manifolds. The entire theory, including the benefits of the symplectic formalism is illustrated with many examples, eventually touching on current research.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Opdracht (ASM)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE) (The final grade (FG) is computed as: FG = 0.6 * FE + 0.3 * HW + IP where IP: 1 point from active participation and work on class assignments HW: average grade (0-10) of the handed-in assignments FE: take-home exam grade (0-10) To pass the course FG needs to be higher than 5.5)
Vaksoort	master
Coördinator	dr. M. Seri
Docent(en)	dr. M. Seri
Verplichte literatuur	Titel Auteur ISBN Prijs Non-compulsory: Mathematical Methods of Classical Mechanics. GTM 60, 2nd ed. Springer-Verlag 1989. DOI 10.1007/978-1-4757-2063-1 V.I. Arnold 978-1-4419-3087-3 Non-compulsory: Mathematical Physics: Classical Mechanics. Springer-Verlag 2018. Institutional access to electronic version available via SpringerLink. DOI: 10.1007/978-3-662-55774-7 A. Knauf 978-3-662-55772-
Entreevoorwaarden	Knowledge assumed: good knowledge of ordinary differential equations and being acquainted with analysis on manifolds, against a general bachelor background in mathematics. Mechanics is not required, but is of course useful.
Opmerkingen	This course was registered last year with course code WIYHM-12
Opgenomen in	Opleiding Jaar Periode Type MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester II a MSc Mathematics and Physics (double degree)  (Mathematics and Complex Dynamical Systems (40 ects)) - semester II a keuzegroep MSc Mathematics: Mathematics and Complex Dynamical Systems - semester II a keuzegroep MSc Mathematics: Science, Business and Policy  (Science, Business and Policy: Mathematics and Complex Dynamical Systems) - semester II a keuzegroep MSc Physics: Quantum Universe  ( Keuzevakken in Theoretical Physics) - semester II a keuze: TP