Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Informatică
Programul de studii: Informatică - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MME0002	Dynamical Systems	

Semester	Hours: C+S+L+P	Category	Status	
2	2+1+1+0	fundamental	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
BUICA Adriana	Ph.D.	Assoc.Prof.	Applied Mathematics	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Introduction to the basic problems of dynamical systems and mathematical modeling	

IV. Course contents
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)

V. 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.

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. 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.	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. BUICA Adriana, Ph.D.