Pertubation Theory (22/23)
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WMMA03205 
Vaknaam  Pertubation Theory (22/23) 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Pertubation Theory (tweejaarlijks 22/23)  
Leerdoelen  At the end of the course, the student is able to: 1. Distinguish when a perturbation is regular or singular 2. Compute the asymptotic expansion of a solution and verify its validity as a solution of a perturbation problem 3. Determine if a given model is structurally stable 4. Identify and apply appropriate perturbation methods/techniques/results (such as averaging, WKB, Fenichel, KAM, etc.) to specific examples 5. Compute normal forms of specific model examples 6. Identify the types of bifurcations present on specific model examples 7. Carryout a local analysis of a bifurcation of a point 8. Formulate the main results of perturbation theory and persistence results in several contexts such as Hamiltonian systems, gradient systems, multitime scale systems, etc. 

Omschrijving  Brief description of the course Please provide a short and to the point description of your course (max. 2000 characters). Briefly describe the content of the course unit. You can use the same text that is used in Ocasys (copy the text under the heading ‘Overview’). If the ocasys text is outdated or insufficient in covering the course’s description, you can update it by using the field below. Perturbation theory, having its roots in the celestial mechanics, is concerned with the study of dynamical systems by viewing these as perturbations of systems that are “simpler” or “ideal”, in the sense that the latter are solvable and/or wellunderstood. The main objective of perturbation theory is to approximate a dynamical system by a more manageable one, regarding the former as a “small” perturbation of the latter. With such an idea, one aims at deducing dynamical properties of the “perturbed system” from the “unperturbed” one. In this course, concepts like “ideal system”, or “perturbation”, among others, are made rigorous. Our goal is to provide an introduction to several useful perturbation methods and to the fundamental results of regular and of singular perturbation theory. Along the course we shall cover several examples appearing in physical and life sciences 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Practisch werk (PR), Schriftelijk tentamen (WE)
(The two takehome exams account for up to 8/10 points (max. 4 points each) of the final grade. The remaining of the 2/10 points are obtained by actively participating in the tutorial sessions. Although attendance is not mandatory to pass the course, to be eligible for the 2/10 points, a student must proactively attend at least 4/8 tutorial sessions.) 

Vaksoort  master  
Coördinator  dr. H. Jardon Kojakhmetov  
Docent(en)  dr. H. Jardon Kojakhmetov  
Verplichte literatuur 


Entreevoorwaarden  The course assumes knowledge from: Mathematics Bachelor and the course Dynamical Systems  
Opmerkingen  
Opgenomen in 
