Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MME0002	Dynamical Systems	

Section	Sem.	Hours: C+S+L	Category	Type	
Mathematics - in Hungarian	5	2+1+0	speciality	optional	
Computer Science	2	2+1+1	fundamental	compulsory	
Mathematics-Computer Science - in Hungarian	5	2+1+0	speciality	optional	

Teaching Staff in Charge	Lect. SERBAN Marcel Adrian, Ph.D., mserban@math.ubbcluj.ro
Assoc.Prof. BUICA Adriana, Ph.D., abuica@math.ubbcluj.ro
Lect. ANDRAS Szilard Karoly, andrasz@math.ubbcluj.ro
Assoc.Prof. SÁNDOR Jozsef, Ph.D., jsandor@math.ubbcluj.ro	
Aims	Introduction to the basic problems of dynamical systems and mathematical modeling	
Content	Introduction (basic terminology, examples, computers and dynamical systems)
Unit I: Discrete and continuous dynamical systems (recurrences and ordinary differential equations as dynamical systems, first order equations, higher order differential equations, existence theorems, general linear ordinary differential equations, boundary value problems)
Unit II: Qualitative Analysis (limit sets, singular points, stability theory, invariant sets, Poincaré maps, bifurcation theory)
Unit III: Numerical Approach (approximate solutions, numerical stability, continuation, calculation of the bifurcation behavior, chaos)
	
Bibliography	1. V. Barbu, Ecuaţii diferenţiale, Junimea, Iaşi, 1985.
2. I. A. Rus, Ecuaţii diferenţiale, ecuaţii integrale şi sisteme dinamice, Transilvania Press, Cluj-Napoca, 1996.
3. M.A. Şerban, Ecuaţii şi sisteme de  ecuaţii diferenţiale, Presa Universitară Clujană, 2009.
4. G. Micula, P. Pavel, Ecuaţii diferenţiale şi integrale prin probleme şi exerciţii, Dacia, Cluj-Napoca, 1989 (culegere de probleme).
5. G. Moroşanu, Ecuaţii diferenţiale. Aplicaţii, Ed. Academiei, 1989, (culegere de probleme).
6. D. Trif, Metode numerice în teoria sistemelor dinamice, Transilvania Press, 1997.
	
Assessment	1. A test paper on seminar: 10% from the final grade
2. A test paper on laboratory: 10% from the final grade
3. Final exam: 80% from the final grade.