6 ECTS credits
150 h study time

Offer 1 with catalog number 4021564DNR for all students in the 1st semester at a (D) Master - preliminary level.

Semester
1st semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Taught in
English
Partnership Agreement
Under interuniversity agreement for degree program
Faculty
Faculty of Science and Bio-engineering Sciences
Department
Mathematics
External partners
Universiteit Antwerpen
Educational team
Decaan WE (course titular)
Activities and contact hours

30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

1)  Definition of Hamiltonian systems, fundamental properties, examples. 


2)  Integrability in finite dimensions (Frobenius, Liouville, extensions), fundamental
properties, examples and differences. 


3)  Important integrable Hamiltonian systemens in mathematics and physisc: sferical 
pendulum, rigid body, spinning top (Lagrange, Euler, Kovalevskaya), coupled spin-oscillators, coupled angular momenta... 


4)  Local behavior in regular points: theorem of Arnold-Liouville, transformation to 
action-angle coördinates. 


5)  Local beahviour in singular points: Eliasson-Miranda-Zung normal form for 
nondegenerate hyperbolic, elliptic and focus-focus components of singular 
points. 


6)  Semitoric systems: properties and interactions with the topology and geometry of the 
underlying manifold. 


7)  Integrability in infinite dimensions (“integrable Hamiltonian PDE”): motivation
important examples (Korteweg-de Vries equation, Sine-Gordon equation, Nonlinear Schrödinger equation).

Additional info

Essential information (schedule, literature/ lecture notes, homeworks etc.) will be posted on the webpage of the professor and/or assistant.

Learning Outcomes

General competences

Good knowledge of the standard results and examples of finite dimensional integrable systems plus insights into infinite dimensional integrability. For details, see the list of content.

Grading

The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.

Within the Other Exam category, the following assignments need to be completed:

  • Other exam with a relative weight of 1 which comprises 100% of the final mark.

Additional info regarding evaluation

1 oral exam at the end of the semester (= in exam period),

several homeworks during the semester, graded by the assistent,

2nd chance exam for the oral exam, but not for the homeworks.

Grade = 75% oral exam + 25% homework results.

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)
Master of Teaching in Science and Technology: wiskunde (120 ECTS, Etterbeek) (only offered in Dutch)